diff --git a/src/zennit/composites.py b/src/zennit/composites.py
index 2129080..f49ef8e 100644
--- a/src/zennit/composites.py
+++ b/src/zennit/composites.py
@@ -162,11 +162,15 @@ class EpsilonGammaBox(SpecialFirstLayerMapComposite):
         A tensor with the same size as the input, describing the lowest possible pixel values.
     high: obj:`torch.Tensor`
         A tensor with the same size as the input, describing the highest possible pixel values.
+    epsilon: float
+        Epsilon parameter for the epsilon rule.
+    gamma: float
+        Gamma parameter for the gamma rule.
     '''
-    def __init__(self, low, high, canonizers=None):
+    def __init__(self, low, high, epsilon=1e-6, gamma=0.25, canonizers=None):
         layer_map = LAYER_MAP_BASE + [
-            (Convolution, Gamma(gamma=0.25)),
-            (torch.nn.Linear, Epsilon()),
+            (Convolution, Gamma(gamma=gamma)),
+            (torch.nn.Linear, Epsilon(epsilon=epsilon)),
         ]
         first_map = [
             (Convolution, ZBox(low, high))
@@ -178,11 +182,16 @@ def __init__(self, low, high, canonizers=None):
 class EpsilonPlus(LayerMapComposite):
     '''An explicit composite using the zplus rule for all convolutional layers and the epsilon rule for all fully
     connected layers.
+
+    Parameters
+    ----------
+    epsilon: float
+        Epsilon parameter for the epsilon rule.
     '''
-    def __init__(self, canonizers=None):
+    def __init__(self, epsilon=1e-6, canonizers=None):
         layer_map = LAYER_MAP_BASE + [
             (Convolution, ZPlus()),
-            (torch.nn.Linear, Epsilon()),
+            (torch.nn.Linear, Epsilon(epsilon=epsilon)),
         ]
         super().__init__(layer_map, canonizers=canonizers)
 
@@ -191,11 +200,16 @@ def __init__(self, canonizers=None):
 class EpsilonAlpha2Beta1(LayerMapComposite):
     '''An explicit composite using the alpha2-beta1 rule for all convolutional layers and the epsilon rule for all
     fully connected layers.
+
+    Parameters
+    ----------
+    epsilon: float
+        Epsilon parameter for the epsilon rule.
     '''
-    def __init__(self, canonizers=None):
+    def __init__(self, epsilon=1e-6, canonizers=None):
         layer_map = LAYER_MAP_BASE + [
             (Convolution, AlphaBeta(alpha=2, beta=1)),
-            (torch.nn.Linear, Epsilon()),
+            (torch.nn.Linear, Epsilon(epsilon=epsilon)),
         ]
         super().__init__(layer_map, canonizers=canonizers)
 
@@ -204,11 +218,16 @@ def __init__(self, canonizers=None):
 class EpsilonPlusFlat(SpecialFirstLayerMapComposite):
     '''An explicit composite using the flat rule for any linear first layer, the zplus rule for all other convolutional
     layers and the epsilon rule for all other fully connected layers.
+
+    Parameters
+    ----------
+    epsilon: float
+        Epsilon parameter for the epsilon rule.
     '''
-    def __init__(self, canonizers=None):
+    def __init__(self, epsilon=1e-6, canonizers=None):
         layer_map = LAYER_MAP_BASE + [
             (Convolution, ZPlus()),
-            (torch.nn.Linear, Epsilon()),
+            (torch.nn.Linear, Epsilon(epsilon=epsilon)),
         ]
         first_map = [
             (Linear, Flat())
@@ -220,11 +239,16 @@ def __init__(self, canonizers=None):
 class EpsilonAlpha2Beta1Flat(SpecialFirstLayerMapComposite):
     '''An explicit composite using the flat rule for any linear first layer, the alpha2-beta1 rule for all other
     convolutional layers and the epsilon rule for all other fully connected layers.
+
+    Parameters
+    ----------
+    epsilon: float
+        Epsilon parameter for the epsilon rule.
     '''
-    def __init__(self, canonizers=None):
+    def __init__(self, epsilon=1e-6, canonizers=None):
         layer_map = LAYER_MAP_BASE + [
             (Convolution, AlphaBeta(alpha=2, beta=1)),
-            (torch.nn.Linear, Epsilon()),
+            (torch.nn.Linear, Epsilon(epsilon=epsilon)),
         ]
         first_map = [
             (Linear, Flat())