diff --git a/test/MOI_wrapper.jl b/test/MOI_wrapper.jl
index ef16ab0..464d069 100644
--- a/test/MOI_wrapper.jl
+++ b/test/MOI_wrapper.jl
@@ -41,15 +41,9 @@ function test_options()
 end
 
 function test_runtests()
-    model = MOI.Utilities.CachingOptimizer(
-        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
-        MOI.instantiate(SDPA.Optimizer; with_bridge_type = Float64),
-    )
+    model = MOI.instantiate(SDPA.Optimizer; with_bridge_type = Float64)
     # `Variable.ZerosBridge` makes dual needed by some tests fail.
-    MOI.Bridges.remove_bridge(
-        model.optimizer,
-        MOI.Bridges.Variable.ZerosBridge{Float64},
-    )
+    MOI.Bridges.remove_bridge(model, MOI.Bridges.Variable.ZerosBridge{Float64})
     MOI.set(model, MOI.Silent(), true)
     MOI.Test.runtests(
         model,
@@ -63,52 +57,47 @@ function test_runtests()
                 MOI.SolverVersion,
             ],
         );
-        exclude = String[
-            # Unable to bridge RotatedSecondOrderCone to PSD because the dimension is too small: got 2, expected >= 3.
-            "test_conic_SecondOrderCone_INFEASIBLE",
-            "test_constraint_PrimalStart_DualStart_SecondOrderCone",
+        exclude = Regex[
             # Expression: MOI.get(model, MOI.TerminationStatus()) == MOI.INFEASIBLE
             #  Evaluated: MathOptInterface.INFEASIBLE_OR_UNBOUNDED == MathOptInterface.INFEASIBLE
-            "test_conic_NormInfinityCone_INFEASIBLE",
-            "test_conic_NormOneCone_INFEASIBLE",
+            r"test_conic_NormInfinityCone_INFEASIBLE$",
+            r"test_conic_NormOneCone_INFEASIBLE$",
+            r"test_conic_SecondOrderCone_INFEASIBLE$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_EqualTo_lower$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_EqualTo_upper$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_GreaterThan$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_Interval_lower$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_Interval_upper$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_LessThan$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_VariableIndex_LessThan$",
+            r"test_solve_DualStatus_INFEASIBILITY_CERTIFICATE_VariableIndex_LessThan_max$",
             # Incorrect objective
             # See https://github.com/jump-dev/MathOptInterface.jl/issues/1759
-            "test_unbounded_MIN_SENSE",
-            "test_unbounded_MIN_SENSE_offset",
-            "test_unbounded_MAX_SENSE",
-            "test_unbounded_MAX_SENSE_offset",
-            "test_infeasible_MAX_SENSE",
-            "test_infeasible_MAX_SENSE_offset",
-            "test_infeasible_MIN_SENSE",
-            "test_infeasible_MIN_SENSE_offset",
-            "test_infeasible_affine_MAX_SENSE",
-            "test_infeasible_affine_MAX_SENSE_offset",
-            "test_infeasible_affine_MIN_SENSE",
-            "test_infeasible_affine_MIN_SENSE_offset",
-            # TODO remove when PR merged
-            # See https://github.com/jump-dev/MathOptInterface.jl/pull/1769
-            "test_objective_ObjectiveFunction_blank",
-            # FIXME investigate
-            #  Expression: isapprox(MOI.get(model, MOI.ObjectiveValue()), T(2), config)
-            #   Evaluated: isapprox(5.999999984012059, 2.0, ...
-            "test_modification_delete_variables_in_a_batch",
+            r"test_unbounded_MIN_SENSE$",
+            r"test_unbounded_MIN_SENSE_offset$",
+            r"test_unbounded_MAX_SENSE$",
+            r"test_unbounded_MAX_SENSE_offset$",
+            r"test_infeasible_MAX_SENSE$",
+            r"test_infeasible_MAX_SENSE_offset$",
+            r"test_infeasible_MIN_SENSE$",
+            r"test_infeasible_MIN_SENSE_offset$",
+            r"test_infeasible_affine_MAX_SENSE$",
+            r"test_infeasible_affine_MAX_SENSE_offset$",
+            r"test_infeasible_affine_MIN_SENSE$",
+            r"test_infeasible_affine_MIN_SENSE_offset$",
             # FIXME investigate
             #  Expression: isapprox(MOI.get(model, MOI.ObjectiveValue()), objective_value, config)
             #   Evaluated: isapprox(-2.1881334077988868e-7, 5.0, ...
-            "test_objective_qp_ObjectiveFunction_edge_case",
+            r"test_objective_qp_ObjectiveFunction_edge_case$",
             # FIXME investigate
             #  Expression: isapprox(MOI.get(model, MOI.ObjectiveValue()), objective_value, config)
             #   Evaluated: isapprox(-2.1881334077988868e-7, 5.0, ...
-            "test_objective_qp_ObjectiveFunction_zero_ofdiag",
-            # FIXME investigate
-            #  Expression: isapprox(MOI.get(model, MOI.ConstraintPrimal(), index), solution_value, config)
-            #   Evaluated: isapprox(2.5058846553349667e-8, 1.0, ...
-            "test_variable_solve_with_lowerbound",
+            r"test_objective_qp_ObjectiveFunction_zero_ofdiag$",
             # FIXME investigate
             # See https://github.com/jump-dev/SDPA.jl/runs/7246518765?check_suite_focus=true#step:6:128
             # Expression: ≈(MOI.get(model, MOI.ConstraintDual(), c), T[1, 0, 0, -1, 1, 0, -1, -1, 1] / T(3), config)
             #  Evaluated: ≈([0.3333333625488728, -0.16666659692134123, -0.16666659693012292, -0.16666659692134123, 0.33333336253987234, -0.16666659692112254, -0.16666659693012292, -0.16666659692112254, 0.333333362548654], [0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, 0.0, -0.3333333333333333, -0.3333333333333333, 0.3333333333333333]
-            "test_conic_PositiveSemidefiniteConeSquare_3",
+            r"test_conic_PositiveSemidefiniteConeSquare_3$",
         ],
     )
     return