diff --git a/docs/source/algorithms.md b/docs/source/algorithms.md
index f60a64afa..04be86d3c 100644
--- a/docs/source/algorithms.md
+++ b/docs/source/algorithms.md
@@ -578,25 +578,34 @@ We implement a few algorithms from scratch. They are currently considered experi
 
         "bhhh"
 
-    Minimize a likelihood function using the BHHH algorithm.
+    Minimize a likelihood function using the box-constraint BHHH algorithm.
 
     BHHH (:cite:`Berndt1974`) can - and should ONLY - be used for minimizing
-    (or maximizing) a likelihood. It is similar to the Newton-Raphson
+    (or maximizing) a likelihood function. It is similar to the Newton-Raphson
     algorithm, but replaces the Hessian matrix with the outer product of the
     gradient. This approximation is based on the information matrix equality
     (:cite:`Halbert1982`) and is thus only vaid when minimizing (or maximizing)
     a likelihood.
 
+    Bounds, i.e. box constraints, are supported. In order to identify the active
+    constraints in the set of inequality constraints, an epsilon-active-set approach is
+    used (see, e.g. :cite:`Nocedal2006`, p. 308, for the active-set method in general and
+    :cite:`Kelley1999`, p. 97, on the estimation of epsilon-active sets a la the
+    Projected BFGS–Armijo algorithm).
+
     The criterion function :func:`func` should return a dictionary with
     at least the entry ``{"contributions": array_or_pytree}`` where ``array_or_pytree``
     contains the likelihood contributions of each individual.
 
     bhhh supports the following options:
 
-    - **convergence_absolute_gradient_tolerance** (float): Stopping criterion for the
-      gradient tolerance. Default is 1e-8.
-    - **stopping_max_iterations** (int): Maximum number of iterations.
-      If reached, terminate. Default is 200.
+    - **convergence.relative_params_tolerance** (float): Stop when the relative movement
+            between parameter vectors is smaller than this. The default is 1e-8.
+    - **convergence.absolute_gradient_tolerance** (float): Stop if all elements of the
+            projected gradient are smaller than this. The default is 1e-8.
+    - **stopping.max_iterations** (int): If the maximum number of iterations is reached,
+      the optimization stops, but we do not count this as convergence.
+      The default is 200.
 
 ```
 
diff --git a/docs/source/refs.bib b/docs/source/refs.bib
index 0ee68d3d3..bbc713ac0 100644
--- a/docs/source/refs.bib
+++ b/docs/source/refs.bib
@@ -884,4 +884,13 @@ @article{Zhang2010
 URL = {https://doi.org/10.1137/09075531X},
 }
 
+@book{Kelley1999,
+author = {Kelley, C. T.},
+title = {Iterative Methods for Optimization},
+publisher = {Society for Industrial and Applied Mathematics},
+year = {1999},
+doi = {10.1137/1.9781611970920},
+URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611970920},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}
diff --git a/src/estimagic/optimization/bhhh.py b/src/estimagic/optimization/bhhh.py
index 6e09412bd..f3c0a7fcc 100644
--- a/src/estimagic/optimization/bhhh.py
+++ b/src/estimagic/optimization/bhhh.py
@@ -1,4 +1,4 @@
-"""Implement Berndt-Hall-Hall-Hausman (BHHH) algorithm."""
+"""Implement the Berndt-Hall-Hall-Hausman (BHHH) algorithm."""
 import numpy as np
 from estimagic.decorators import mark_minimizer
 
@@ -12,111 +12,354 @@
 def bhhh(
     criterion_and_derivative,
     x,
+    lower_bounds,
+    upper_bounds,
     *,
     convergence_absolute_gradient_tolerance=1e-8,
+    convergence_relative_params_tolerance=1e-8,
     stopping_max_iterations=200,
 ):
-    """Minimize a likelihood function using the BHHH algorithm.
+    """Minimize a likelihood function using the box-constrained BHHH algorithm.
 
     For details, see :ref:`_own_algorithms`.
     """
-    result_dict = bhhh_internal(
-        criterion_and_derivative,
-        x=x,
-        convergence_absolute_gradient_tolerance=convergence_absolute_gradient_tolerance,
-        stopping_max_iterations=stopping_max_iterations,
-    )
+    if np.isinf(lower_bounds).all() and np.isinf(upper_bounds).all():
+        result_dict = bhhh_unconstrained(
+            criterion_and_derivative,
+            x,
+            convergence_relative_params_tolerance,
+            convergence_absolute_gradient_tolerance,
+            stopping_max_iterations,
+        )
+    else:
+        result_dict = bhhh_box_constrained(
+            criterion_and_derivative,
+            x,
+            lower_bounds,
+            upper_bounds,
+            convergence_relative_params_tolerance,
+            convergence_absolute_gradient_tolerance,
+            stopping_max_iterations,
+        )
 
     return result_dict
 
 
-def bhhh_internal(
+def bhhh_unconstrained(
     criterion_and_derivative,
     x,
+    convergence_relative_params_tolerance,
     convergence_absolute_gradient_tolerance,
     stopping_max_iterations,
 ):
-    """Minimize a likelihood function using the BHHH algorithm.
+    """Minimize a likelihood function using the unconstrained BHHH algorithm.
+
+    This implementation is based on the Matlab code by Fedor Iskhakov, which can
+    be found on his `Github page <https://github.com/fediskhakov/MPECvsNFXP/blob/
+    8212346a0426f54977823bd754947f528ed749ba/nfxp_Rust87/nfxp.m#L315>`.
 
     Args:
-        criterion_and_derivative (callable): The objective function to be minimized.
-        x (np.ndarray): Initial guess of the parameter vector (starting points).
-        convergence_absolute_gradient_tolerance (float): Stopping criterion for the
-            gradient tolerance.
-        stopping_max_iterations (int): Maximum number of iterations. If reached,
-            terminate.
+        criterion_and_derivative (callable): A function returning the tuple:
+            - criterion (np.ndarray): Likelihood contributions of shape (n_obs,)
+            - derivative (np.ndarray): Jacobian matrix of shape (n_obs, n_params)
+        x (np.ndarray): Initial guess of the parameter vector x (starting points).
+        lower_bounds (np.ndarray): 1d array of shape (n_params,) with lower bounds
+            for the parameter vector x.
+        upper_bounds (np.ndarray): 1d array of shape (n_params,) with upper bounds
+            for the parameter vector x
+        convergence_relative_params_tolerance (float): Stop when the relative movement
+            between parameter vectors is smaller than this.
+        convergence_absolute_gradient_tolerance (float): Stop if all elements of the
+            gradient are smaller than this.
+        stopping_max_iterations (int): If the maximum number of iterations is reached,
+            the optimization stops, but we do not count this as convergence.
 
     Returns:
-        (dict) Result dictionary containing:
+        dict: Result dictionary containing:
 
-        - solution_x (np.ndarray): Solution vector of shape (n,).
-        - solution_criterion (np.ndarray): Likelihood at the solution. Shape (n_obs,).
+        - solution_x (np.ndarray): Solution vector of shape (n_params,).
+        - solution_criterion (np.ndarray): Likelihood contributions at the solution.
+            Shape (n_obs,).
+        - solution_loglikelihood (float): Value of the log-likelihood at the solution.
         - n_iterations (int): Number of iterations the algorithm ran before finding a
             solution vector or reaching stopping_max_iterations.
         - message (str): Message to the user. Currently it says: "Under development."
     """
-    criterion_accepted, gradient = criterion_and_derivative(x)
-    x_accepted = x
+    _zero_threshold = np.finfo(float).eps
+
+    criterion_accepted, jacobian = criterion_and_derivative(x)
 
-    hessian_approx = np.dot(gradient.T, gradient)
-    gradient_sum = np.sum(gradient, axis=0)
-    direction = np.linalg.solve(hessian_approx, gradient_sum)
-    gtol = np.dot(gradient_sum, direction)
+    gradient = np.sum(jacobian, axis=0)
+    hessian_approx = jacobian.T @ jacobian
+    direction = np.linalg.solve(hessian_approx, gradient)
+
+    norm_grad = gradient @ direction
 
     initial_step_size = 1
     step_size = initial_step_size
 
-    niter = 1
-    while niter < stopping_max_iterations:
-        niter += 1
+    x_candidate = x + step_size * direction
 
-        x_candidate = x_accepted + step_size * direction
-        criterion_candidate, gradient = criterion_and_derivative(x_candidate)
+    converged = False
+    for _n_iter in range(stopping_max_iterations):
 
-        # If previous step was accepted
-        if step_size == initial_step_size:
-            hessian_approx = np.dot(gradient.T, gradient)
+        criterion_candidate, jacobian = criterion_and_derivative(x_candidate)
 
-        else:
-            criterion_candidate, gradient = criterion_and_derivative(x_candidate)
+        if step_size == initial_step_size:
+            hessian_approx = jacobian.T @ jacobian
 
-        # Line search
         if np.sum(criterion_candidate) > np.sum(criterion_accepted):
             step_size /= 2
 
             if step_size <= 0.01:
-                # Accept step
-                x_accepted = x_candidate
+                x = x_candidate
                 criterion_accepted = criterion_candidate
 
-                # Reset step size
                 step_size = initial_step_size
-
-        # If decrease in likelihood, calculate new direction vector
         else:
-            # Accept step
-            x_accepted = x_candidate
+            x = x_candidate
             criterion_accepted = criterion_candidate
 
-            gradient_sum = np.sum(gradient, axis=0)
-            direction = np.linalg.solve(hessian_approx, gradient_sum)
-            gtol = np.dot(gradient_sum, direction)
+            gradient = np.sum(jacobian, axis=0)
+            direction = np.linalg.solve(hessian_approx, gradient)
 
-            if gtol < 0:
-                hessian_approx = np.dot(gradient.T, gradient)
-                direction = np.linalg.solve(hessian_approx, gradient_sum)
+            norm_grad = gradient @ direction
+
+            if norm_grad < 0:
+                hessian_approx = jacobian.T @ jacobian
+                direction = np.linalg.solve(hessian_approx, gradient)
 
-            # Reset stepsize
             step_size = initial_step_size
 
-        if gtol < convergence_absolute_gradient_tolerance:
+        x_candidate = x + step_size * direction
+
+        relative_params_difference = np.max(
+            np.abs(((x_candidate - x)) / (x + _zero_threshold)) / step_size
+        )
+
+        if relative_params_difference < convergence_relative_params_tolerance:
+            converged = True
+            break
+        elif norm_grad < convergence_absolute_gradient_tolerance:
+            converged = True
             break
 
     result_dict = {
-        "solution_x": x_accepted,
+        "solution_x": x,
         "solution_criterion": criterion_accepted,
-        "n_iterations": niter,
+        "solution_loglikelihood": np.sum(criterion_accepted),
+        "converged": converged,
+        "relative_params_difference": relative_params_difference,
+        "absolute_gradient_norm": norm_grad,
+        "n_iterations": _n_iter,
+        "message": "Under develpment",
+    }
+
+    return result_dict
+
+
+def bhhh_box_constrained(
+    criterion_and_derivative,
+    x,
+    lower_bounds,
+    upper_bounds,
+    convergence_relative_params_tolerance,
+    convergence_absolute_gradient_tolerance,
+    stopping_max_iterations,
+):
+    """Minimize a likelihood function using the box-constrained BHHH algorithm.
+
+    The (in)active constraints are identified via an epsilon-active-set method,
+    similar to the approach used by the Projected BFGS-Armijo algorithm
+    (see :cite:`Kelley1999`, p. 97).
+
+    The unconstrained version of this algorithm is based on the Matlab implementation
+    by Adam E. Theising. See `Assignment 4 <https://adamtheising.github.io/aae637>`
+    on Maximum Likelihood Estimation on the course page of Applied Econometrics II.
+
+
+    Args:
+        criterion_and_derivative (callable): A function returning the tuple:
+            - criterion (np.ndarray): Likelihood contributions of shape (n_obs,)
+            - derivative (np.ndarray): Jacobian matrix of shape (n_obs, n_params)
+        x (np.ndarray): Initial guess of the parameter vector x (starting points).
+        lower_bounds (np.ndarray): 1d array of shape (n_params,) with lower bounds
+            for the parameter vector x.
+        upper_bounds (np.ndarray): 1d array of shape (n_params,) with upper bounds
+            for the parameter vector x
+        convergence_relative_params_tolerance (float): Stop when the relative movement
+            between parameter vectors is smaller than this.
+        convergence_absolute_gradient_tolerance (float): Stop if all elements of the
+            projected gradient are smaller than this.
+        stopping_max_iterations (int): If the maximum number of iterations is reached,
+            the optimization stops, but we do not count this as convergence.
+
+    Returns:
+        dict: Result dictionary containing:
+
+        - solution_x (np.ndarray): Solution vector of shape (n_params,).
+        - solution_criterion (np.ndarray): Likelihood contributions at the solution.
+            Shape (n_obs,).
+        - solution_loglikelihood (float): Value of the log-likelihood at the solution.
+        - n_iterations (int): Number of iterations the algorithm ran before finding a
+            solution vector or reaching stopping_max_iterations.
+        - message (str): Message to the user. Currently it says: "Under development."
+    """
+    n_params = len(x)
+    min_step_size = 1e-6
+    _zero_threshold = np.finfo(float).eps
+
+    jacobian = criterion_and_derivative(x, task="derivative")
+    gradient = np.sum(jacobian, axis=0)
+
+    norm_proj_grad = np.linalg.norm(
+        x - np.clip(x - gradient, lower_bounds, upper_bounds)
+    )
+    inactive_set = _estimate_epsilon_inactive_set(
+        x, norm_proj_grad, lower_bounds, upper_bounds
+    )
+
+    converged = False
+    for _n_iter in range(stopping_max_iterations):
+        jacobian = criterion_and_derivative(x, task="derivative")
+        gradient = np.sum(jacobian, axis=0)
+
+        gradient_reduced = gradient[inactive_set]
+        hessian_approx = jacobian.T @ jacobian
+        hessian_reduced = hessian_approx[inactive_set[:, np.newaxis], inactive_set]
+
+        direction_projected = _determine_descent_direction(
+            gradient, gradient_reduced, hessian_reduced, inactive_set, n_params
+        )
+
+        step_size = _find_optimal_step_size(
+            x,
+            direction_projected,
+            lower_bounds,
+            upper_bounds,
+            min_step_size,
+            criterion_and_derivative,
+        )
+
+        x_candidate = np.clip(
+            x + step_size * direction_projected, lower_bounds, upper_bounds
+        )
+        relative_params_difference = np.max(
+            np.abs(((x_candidate - x)) / (x + _zero_threshold)) / step_size
+        )
+        x = x_candidate
+
+        norm_proj_grad = np.linalg.norm(
+            x - np.clip(x - gradient, lower_bounds, upper_bounds)
+        )
+
+        if relative_params_difference < convergence_relative_params_tolerance:
+            converged = True
+            break
+        elif norm_proj_grad < convergence_absolute_gradient_tolerance:
+            converged = True
+            break
+
+        inactive_set = _estimate_epsilon_inactive_set(
+            x, norm_proj_grad, lower_bounds, upper_bounds
+        )
+
+    solution_criterion = criterion_and_derivative(x, task="criterion")
+
+    result_dict = {
+        "solution_x": x,
+        "solution_criterion": solution_criterion,
+        "solution_loglikelihood": np.sum(solution_criterion),
+        "converged": converged,
+        "relative_params_difference": relative_params_difference,
+        "absolute_gradient_norm": norm_proj_grad,
+        "n_iterations": _n_iter,
         "message": "Under develpment",
     }
 
     return result_dict
+
+
+def _estimate_epsilon_inactive_set(x, norm_grad, lower_bounds, upper_bounds):
+    """Estimate the set of epsilon-inactive bound constraints.
+
+    The set of epsilon-inactive indices underestimates (overestimates) the actual
+    set of inactive (active) indices.
+
+    Args:
+        x (np.ndarray): Current parameter vector of shape (n_params,).
+        norm_grad (float): Norm of the projected gradient.
+        lower_bounds (np.ndarray): 1d array of shape (n_params,) with lower bounds
+            for the parameter vector x.
+        upper_bounds (np.ndarray): 1d array of shape (n_params,) with upper bounds
+            for the parameter vector x/
+
+    Returns:
+        np.ndarray: 1d array of shape (n_inactive_constraints,) containing the set
+            of inactive constraints.
+    """
+    epsilon = min(np.min(upper_bounds - lower_bounds) / 2, norm_grad)
+
+    inactive_set = np.where(
+        (lower_bounds + epsilon < x) & (x < upper_bounds - epsilon)
+    )[0]
+
+    return inactive_set
+
+
+def _determine_descent_direction(
+    gradient_candidate, gradient_reduced, hessian_reduced, inactive_set, n_params
+):
+    """Determine the new descent (search) direction."""
+    direction = np.linalg.solve(hessian_reduced, gradient_reduced)
+
+    direction_active = gradient_candidate.copy()
+    direction_active[inactive_set] = 0
+
+    direction_projected = np.zeros(n_params)
+    direction_projected[inactive_set] = direction
+
+    direction_all = direction_active + direction_projected
+
+    return direction_all
+
+
+def _find_optimal_step_size(
+    x,
+    direction_projected,
+    lower_bounds,
+    upper_bounds,
+    min_step_size,
+    criterion_and_derivative,
+):
+    """Find optimal step length."""
+    step_size_trial = 2
+    step_size_optimal = 1
+
+    loglike_full_step = 1
+    loglike_half_step = 0
+
+    while (loglike_full_step > loglike_half_step) & (step_size_trial >= min_step_size):
+        step_size_trial /= 2
+
+        criterion_full_step = criterion_and_derivative(
+            np.clip(
+                x + step_size_trial * direction_projected, lower_bounds, upper_bounds
+            ),
+            task="criterion",
+        )
+        criterion_half_step = criterion_and_derivative(
+            np.clip(
+                x + (step_size_trial / 2) * direction_projected,
+                lower_bounds,
+                upper_bounds,
+            ),
+            task="criterion",
+        )
+
+        loglike_full_step = np.sum(criterion_full_step)
+        loglike_half_step = np.sum(criterion_half_step)
+
+        step_size_optimal = step_size_trial
+
+    return step_size_optimal
diff --git a/tests/optimization/fixtures/telco_churn_clean.csv b/tests/optimization/fixtures/telco_churn_clean.csv
new file mode 100644
index 000000000..cc1fd3b1e
--- /dev/null
+++ b/tests/optimization/fixtures/telco_churn_clean.csv
@@ -0,0 +1,7033 @@
+gender,SeniorCitizen,Partner,Dependents,tenure,PhoneService,PaperlessBilling,MonthlyCharges,Churn
+0,0,1,0,1,0,1,29.85,0
+1,0,0,0,34,1,0,56.95,0
+1,0,0,0,2,1,1,53.85,1
+1,0,0,0,45,0,0,42.3,0
+0,0,0,0,2,1,1,70.7,1
+0,0,0,0,8,1,1,99.65,1
+1,0,0,1,22,1,1,89.1,0
+0,0,0,0,10,0,0,29.75,0
+0,0,1,0,28,1,1,104.8,1
+1,0,0,1,62,1,0,56.15,0
+1,0,1,1,13,1,1,49.95,0
+1,0,0,0,16,1,0,18.95,0
+1,0,1,0,58,1,0,100.35,0
+1,0,0,0,49,1,1,103.7,1
+1,0,0,0,25,1,1,105.5,0
+0,0,1,1,69,1,0,113.25,0
+0,0,0,0,52,1,0,20.65,0
+1,0,0,1,71,1,0,106.7,0
+0,0,1,1,10,1,0,55.2,1
+0,0,0,0,21,1,1,90.05,0
+1,1,0,0,1,0,1,39.65,1
+1,0,1,0,12,1,0,19.8,0
+1,0,0,0,1,1,0,20.15,1
+0,0,1,0,58,1,1,59.9,0
+1,0,1,1,49,1,0,59.6,0
+0,0,0,0,30,1,1,55.3,0
+1,0,1,1,47,1,1,99.35,1
+1,0,1,1,1,0,0,30.2,1
+1,0,1,0,72,1,1,90.25,0
+0,0,0,1,17,1,1,64.7,1
+0,1,1,0,71,1,1,96.35,0
+1,1,1,0,2,1,1,95.5,0
+0,0,1,1,27,1,0,66.15,0
+1,0,0,0,1,1,0,20.2,0
+1,1,0,0,1,1,0,45.25,0
+0,0,1,1,72,1,0,99.9,0
+1,0,0,0,5,1,1,69.7,1
+0,0,0,0,46,1,1,74.8,0
+1,0,0,0,34,1,1,106.35,1
+0,0,0,0,11,1,1,97.85,1
+1,0,1,1,10,1,0,49.55,0
+0,0,1,1,70,1,1,69.2,0
+0,0,1,1,17,1,0,20.75,0
+0,0,0,0,63,1,1,79.85,0
+0,0,1,0,13,1,1,76.2,0
+0,0,0,0,49,1,1,84.5,0
+1,0,0,0,2,1,0,49.25,0
+0,0,0,0,2,1,1,80.65,1
+1,0,0,0,52,1,1,79.75,0
+0,0,1,1,69,1,1,64.15,0
+0,1,0,0,43,1,1,90.25,0
+0,0,0,0,15,1,1,99.1,1
+0,1,1,0,25,1,1,69.5,0
+0,1,1,0,8,1,1,80.65,1
+0,1,1,1,60,1,1,74.85,0
+1,1,0,0,18,1,1,95.45,1
+0,0,1,1,63,1,1,99.65,0
+1,1,1,1,66,1,1,108.45,0
+0,0,1,1,34,1,0,24.95,0
+0,0,0,0,72,1,1,107.5,0
+0,0,1,0,47,1,1,100.5,0
+1,0,0,0,60,1,1,89.9,0
+1,0,1,0,72,0,0,42.1,0
+0,0,1,1,18,1,1,54.4,0
+0,0,0,0,9,1,0,94.4,1
+0,0,0,0,3,1,1,75.3,0
+1,0,1,0,47,1,1,78.9,0
+0,0,0,0,31,1,0,79.2,0
+0,0,1,1,50,1,0,20.15,0
+1,0,0,0,10,1,1,79.85,0
+1,0,0,0,1,1,0,49.05,0
+0,0,1,1,52,1,1,20.4,0
+1,1,1,1,64,1,1,111.6,0
+1,0,1,1,62,1,1,24.25,0
+0,0,0,1,3,1,1,64.5,0
+0,1,0,0,56,1,0,110.5,0
+0,0,0,0,46,1,0,55.65,0
+0,0,1,1,8,1,0,54.65,0
+1,1,0,0,30,1,1,74.75,0
+0,0,1,1,45,1,1,25.9,0
+0,0,0,1,1,1,1,79.35,1
+0,0,1,1,11,0,0,50.55,0
+0,0,1,0,7,1,1,75.15,1
+0,0,0,0,42,1,1,103.8,0
+0,0,1,0,49,1,1,20.15,0
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diff --git a/tests/optimization/test_bhhh.py b/tests/optimization/test_bhhh.py
index 20098635c..1e54eff83 100644
--- a/tests/optimization/test_bhhh.py
+++ b/tests/optimization/test_bhhh.py
@@ -2,9 +2,12 @@
 from functools import partial
 
 import numpy as np
+import pandas as pd
 import pytest
 import statsmodels.api as sm
-from estimagic.optimization.bhhh import bhhh_internal
+from estimagic.config import TEST_FIXTURES_DIR
+from estimagic.optimization.bhhh import bhhh_box_constrained
+from estimagic.optimization.bhhh import bhhh_unconstrained
 from estimagic.utilities import get_rng
 from numpy.testing import assert_array_almost_equal as aaae
 from scipy.stats import norm
@@ -13,7 +16,7 @@
 def generate_test_data():
     rng = get_rng(seed=12)
 
-    num_observations = 5000
+    num_observations = 5_000
     x1 = rng.multivariate_normal([0, 0], [[1, 0.75], [0.75, 1]], num_observations)
     x2 = rng.multivariate_normal([1, 4], [[1, 0.75], [0.75, 1]], num_observations)
 
@@ -27,6 +30,20 @@ def generate_test_data():
     return endog, exog
 
 
+def load_ibm_data():
+    df = pd.read_csv(TEST_FIXTURES_DIR / "telco_churn_clean.csv")
+
+    exog = df.drop(columns="Churn").to_numpy()
+    intercept = np.ones((exog.shape[0], 1))
+    exog = np.hstack((intercept, exog))
+    endog = df[["Churn"]].to_numpy()
+    endog = endog.reshape(
+        len(endog),
+    )
+
+    return endog, exog
+
+
 def _cdf_logit(x):
     return 1 / (1 + np.exp(-x))
 
@@ -62,74 +79,264 @@ def get_score_probit(endog, exog, x):
     return derivative_loglikelihood[:, None] * exog
 
 
-def criterion_and_derivative_logit(x):
+def criterion_and_derivative_logit(x, task="criterion_and_derivative"):
     """Return Logit criterion and derivative.
 
     Args:
         x (np.ndarray): Parameter vector of shape (n_obs,).
+        task (str): If task=="criterion", compute log-likelihood.
+            If task=="derivative", compute derivative.
+            If task="criterion_and_derivative", compute both.
 
     Returns:
-        tuple: first entry is the criterion, second entry is the score
-
+        np.ndarray or tuple: If task=="criterion" it returns the output of
+            criterion, which is a 1d numpy array.
+            If task=="derivative" it returns the first derivative of criterion,
+            which is 2d numpy array.
+            If task=="criterion_and_derivative" it returns both as a tuple.
     """
     endog, exog = generate_test_data()
-    score = partial(get_score_logit, endog, exog)
-    loglike = partial(get_loglikelihood_logit, endog, exog)
+    result = ()
 
-    return -loglike(x), score(x)
+    if "criterion" in task:
+        loglike = partial(get_loglikelihood_logit, endog, exog)
+        result += (-loglike(x),)
+    if "derivative" in task:
+        score = partial(get_score_logit, endog, exog)
+        result += (score(x),)
 
+    if len(result) == 1:
+        (result,) = result
 
-def criterion_and_derivative_probit(x):
-    """Return Probit criterion and derivative.
+    return result
+
+
+def criterion_and_derivative_logit_ibm(x, task="criterion_and_derivative"):
+    """Return Logit criterion and derivative.
 
     Args:
         x (np.ndarray): Parameter vector of shape (n_obs,).
+        task (str): If task=="criterion", compute log-likelihood.
+            If task=="derivative", compute derivative.
+            If task="criterion_and_derivative", compute both.
 
     Returns:
-        tuple: first entry is the criterion, second entry is the score
+        np.ndarray or tuple: If task=="criterion" it returns the output of
+            criterion, which is a 1d numpy array.
+            If task=="derivative" it returns the first derivative of criterion,
+            which is 2d numpy array.
+            If task=="criterion_and_derivative" it returns both as a tuple.
+    """
+    endog, exog = load_ibm_data()
+    result = ()
+
+    if "criterion" in task:
+        loglike = partial(get_loglikelihood_logit, endog, exog)
+        result += (-loglike(x),)
+    if "derivative" in task:
+        score = partial(get_score_logit, endog, exog)
+        result += (score(x),)
+
+    if len(result) == 1:
+        (result,) = result
+
+    return result
+
 
+def criterion_and_derivative_probit(x, task="criterion_and_derivative"):
+    """Return Probit criterion and derivative.
+
+    Args:
+        x (np.ndarray): Parameter vector of shape (n_obs,).
+        task (str): If task=="criterion", compute log-likelihood.
+            If task=="derivative", compute derivative.
+            If task="criterion_and_derivative", compute both.
+
+    Returns:
+        np.ndarray or tuple: If task=="criterion" it returns the output of
+            criterion, which is a 1d numpy array.
+            If task=="derivative" it returns the first derivative of criterion,
+            which is 2d numpy array.
+            If task=="criterion_and_derivative" it returns both as a tuple.
     """
     endog, exog = generate_test_data()
+    result = ()
+
+    if "criterion" in task:
+        loglike = partial(get_loglikelihood_probit, endog, exog)
+        result += (-loglike(x),)
+    if "derivative" in task:
+        score = partial(get_score_probit, endog, exog)
+        result += (score(x),)
+
+    if len(result) == 1:
+        (result,) = result
+
+    return result
+
+
+def criterion_and_derivative_probit_ibm(x, task="criterion_and_derivative"):
+    """Return Probit criterion and derivative.
+
+    Args:
+        x (np.ndarray): Parameter vector of shape (n_obs,).
+        task (str): If task=="criterion", compute log-likelihood.
+            If task=="derivative", compute derivative.
+            If task="criterion_and_derivative", compute both.
 
-    score = partial(get_score_probit, endog, exog)
-    loglike = partial(get_loglikelihood_probit, endog, exog)
+    Returns:
+        np.ndarray or tuple: If task=="criterion" it returns the output of
+            criterion, which is a 1d numpy array.
+            If task=="derivative" it returns the first derivative of criterion,
+            which is 2d numpy array.
+            If task=="criterion_and_derivative" it returns both as a tuple.
+    """
+    endog, exog = load_ibm_data()
+    result = ()
+
+    if "criterion" in task:
+        loglike = partial(get_loglikelihood_probit, endog, exog)
+        result += (-loglike(x),)
+    if "derivative" in task:
+        score = partial(get_score_probit, endog, exog)
+        result += (score(x),)
 
-    return -loglike(x), score(x)
+    if len(result) == 1:
+        (result,) = result
+
+    return result
+
+
+# =====================================================================================
+# Fixtures
+# =====================================================================================
 
 
 @pytest.fixture
-def result_statsmodels_logit():
+def result_logit_unconstrained():
     endog, exog = generate_test_data()
-    result = sm.Logit(endog, exog).fit()
+    result = sm.Logit(endog, exog).fit(disp=True)
 
-    return result
+    return result.params
 
 
 @pytest.fixture
-def result_statsmodels_probit():
+def result_probit_unconstrained():
     endog, exog = generate_test_data()
-    result = sm.Probit(endog, exog).fit()
+    result = sm.Probit(endog, exog).fit(disp=True)
+
+    return result.params
+
+
+@pytest.fixture
+def result_logit_ibm():
+    endog, exog = load_ibm_data()
+    result = sm.Logit(endog, exog).fit(disp=False)
+
+    return result.params
+
+
+@pytest.fixture
+def result_probit_ibm():
+    endog, exog = load_ibm_data()
+    result = sm.Probit(endog, exog).fit(disp=False)
+
+    return result.params
 
-    return result
+
+@pytest.fixture
+def result_logit_constrained():
+    endog, exog = generate_test_data()
+    result = sm.Logit(endog, exog).fit(
+        method="lbfgs", bounds=((-5, 10), (-100, 100), (-100, 100)), disp=False
+    )
+
+    return result.params
+
+
+# =====================================================================================
+# Tests
+# =====================================================================================
+TEST_CASES_UNCONSTRAINED = [
+    (criterion_and_derivative_logit, 3, "result_logit_unconstrained", 1e-6, 0),
+    (criterion_and_derivative_logit, 3, "result_logit_unconstrained", 0, 1e-8),
+    (criterion_and_derivative_probit, 3, "result_probit_unconstrained", 1e-6, 0),
+    (criterion_and_derivative_probit, 3, "result_probit_unconstrained", 0, 1e-8),
+    (criterion_and_derivative_logit_ibm, 9, "result_logit_ibm", 1e-6, 0),
+    (criterion_and_derivative_logit_ibm, 9, "result_logit_ibm", 0, 1e-8),
+    (criterion_and_derivative_probit_ibm, 9, "result_probit_ibm", 1e-6, 0),
+    (criterion_and_derivative_probit_ibm, 9, "result_probit_ibm", 0, 1e-8),
+]
 
 
 @pytest.mark.parametrize(
-    "criterion_and_derivative, result_statsmodels",
-    [
-        (criterion_and_derivative_logit, "result_statsmodels_logit"),
-        (criterion_and_derivative_probit, "result_statsmodels_probit"),
-    ],
+    "criterion_and_derivative, n_params, expected, params_tol, gradient_tol",
+    TEST_CASES_UNCONSTRAINED,
 )
-def test_maximum_likelihood(criterion_and_derivative, result_statsmodels, request):
-    result_expected = request.getfixturevalue(result_statsmodels)
+def test_maximum_likelihood_unconstrained(
+    criterion_and_derivative,
+    n_params,
+    expected,
+    params_tol,
+    gradient_tol,
+    request,
+):
+    params_expected = request.getfixturevalue(expected)
+
+    result_unconstr = bhhh_unconstrained(
+        criterion_and_derivative,
+        x=np.zeros(n_params),
+        convergence_relative_params_tolerance=params_tol,
+        convergence_absolute_gradient_tolerance=gradient_tol,
+        stopping_max_iterations=200,
+    )
+    result_constr = bhhh_box_constrained(
+        criterion_and_derivative,
+        x=np.zeros(n_params),
+        lower_bounds=np.full(n_params, -np.inf),
+        upper_bounds=np.full(n_params, np.inf),
+        convergence_relative_params_tolerance=params_tol,
+        convergence_absolute_gradient_tolerance=gradient_tol,
+        stopping_max_iterations=200,
+    )
+
+    aaae(result_unconstr["solution_x"], params_expected, decimal=4)
+    aaae(result_constr["solution_x"], params_expected, decimal=4)
 
-    x = np.zeros(3)
 
-    result_bhhh = bhhh_internal(
+TEST_CASES_CONSTRAINED = [
+    (
+        criterion_and_derivative_logit,
+        np.zeros(3),
+        np.array([-5, -100, -100]),
+        np.array([10, 100, 100]),
+        "result_logit_constrained",
+    ),
+]
+
+
+@pytest.mark.parametrize(
+    "criterion_and_derivative, x0, lower_bounds, upper_bounds, expected",
+    TEST_CASES_CONSTRAINED,
+)
+def test_maximum_likelihood_constrained(
+    criterion_and_derivative,
+    x0,
+    lower_bounds,
+    upper_bounds,
+    expected,
+    request,
+):
+    params_expected = request.getfixturevalue(expected)
+
+    result = bhhh_box_constrained(
         criterion_and_derivative,
-        x=x,
-        convergence_absolute_gradient_tolerance=1e-8,
+        x=x0,
+        lower_bounds=lower_bounds,
+        upper_bounds=upper_bounds,
+        convergence_relative_params_tolerance=1e-4,
+        convergence_absolute_gradient_tolerance=1e-4,
         stopping_max_iterations=200,
     )
 
-    aaae(result_bhhh["solution_x"], result_expected.params, decimal=4)
+    aaae(result["solution_x"], params_expected, decimal=4)
diff --git a/tests/optimization/test_pounders_integration.py b/tests/optimization/test_pounders_integration.py
index ea289b1ec..1a7a9919e 100644
--- a/tests/optimization/test_pounders_integration.py
+++ b/tests/optimization/test_pounders_integration.py
@@ -11,23 +11,6 @@
 from numpy.testing import assert_array_almost_equal as aaae
 
 
-def load_history(start_vec, solver_sub):
-    start_vec_str = np.array2string(
-        start_vec, precision=3, separator=",", suppress_small=False
-    )
-
-    history_x = np.genfromtxt(
-        TEST_FIXTURES_DIR / f"history_x_{start_vec_str}_{solver_sub}_3_8.csv",
-        delimiter=",",
-    )
-    history_criterion = np.genfromtxt(
-        TEST_FIXTURES_DIR / f"history_criterion_{start_vec_str}_{solver_sub}_3_8.csv",
-        delimiter=",",
-    )
-
-    return history_x, history_criterion
-
-
 @pytest.fixture
 def criterion():
     data = pd.read_csv(TEST_FIXTURES_DIR / "pounders_example_data.csv")