diff --git a/diffprivlib/models/forest.py b/diffprivlib/models/forest.py
index 042c61c..4b131fd 100644
--- a/diffprivlib/models/forest.py
+++ b/diffprivlib/models/forest.py
@@ -345,7 +345,7 @@ class DecisionTreeClassifier(skDecisionTreeClassifier, DiffprivlibMixin):
         skDecisionTreeClassifier, "max_depth", "random_state")
 
     def __init__(self, max_depth=5, *, epsilon=1, bounds=None, classes=None, random_state=None, accountant=None,
-                 **unused_args):
+                 criterion=None, **unused_args):
         # Todo: Remove when scikit-learn v1.0 is a min requirement
         try:
             super().__init__(  # pylint: disable=unexpected-keyword-arg
@@ -378,6 +378,7 @@ def __init__(self, max_depth=5, *, epsilon=1, bounds=None, classes=None, random_
         self.bounds = bounds
         self.classes = classes
         self.accountant = BudgetAccountant.load_default(accountant)
+        del criterion
 
         self._warn_unused_args(unused_args)
 
@@ -448,6 +449,11 @@ def fit(self, X, y, sample_weight=None, check_input=True):
 
         return self
 
+    def _fit(self, X, y, sample_weight=None, check_input=True, missing_values_in_feature_mask=None):
+        self.fit(X, y, sample_weight=sample_weight, check_input=check_input)
+
+        return self
+
     @property
     def n_features_(self):
         return self.n_features_in_
diff --git a/diffprivlib/models/logistic_regression.py b/diffprivlib/models/logistic_regression.py
index 112ea9f..82294ad 100644
--- a/diffprivlib/models/logistic_regression.py
+++ b/diffprivlib/models/logistic_regression.py
@@ -371,7 +371,7 @@ def _logistic_regression_path(X, y, epsilon, data_norm, pos_class=None, Cs=10, f
         X = check_array(X, accept_sparse='csr', dtype=np.float64, accept_large_sparse=True)
         y = check_array(y, ensure_2d=False, dtype=None)
         check_consistent_length(X, y)
-    _, n_features = X.shape
+    n_samples, n_features = X.shape
 
     classes = np.unique(y)
 
@@ -400,17 +400,20 @@ def _logistic_regression_path(X, y, epsilon, data_norm, pos_class=None, Cs=10, f
 
     if SKL_LOSS_MODULE:
         func = LinearModelLoss(base_loss=HalfBinomialLoss(), fit_intercept=fit_intercept).loss_gradient
+        sw_sum = n_samples
     else:
         func = _logistic_loss_and_grad
+        sw_sum = 1
 
     coefs = []
     n_iter = np.zeros(len(Cs), dtype=np.int32)
     for i, C in enumerate(Cs):
-        vector_mech = Vector(epsilon=epsilon, dimension=n_features + int(fit_intercept), alpha=1. / C,
+        l2_reg_strength = 1.0 / (C * sw_sum)
+        vector_mech = Vector(epsilon=epsilon, dimension=n_features + int(fit_intercept), alpha=l2_reg_strength,
                              function_sensitivity=0.25, data_sensitivity=data_norm, random_state=random_state)
         noisy_logistic_loss = vector_mech.randomise(func)
 
-        args = (X, target, sample_weight, 1. / C) if SKL_LOSS_MODULE else (X, target, 1. / C, sample_weight)
+        args = (X, target, sample_weight, l2_reg_strength) if SKL_LOSS_MODULE else (X, target, l2_reg_strength, sample_weight)
 
         iprint = [-1, 50, 1, 100, 101][np.searchsorted(np.array([0, 1, 2, 3]), verbose)]
         output_vec, _, info = optimize.fmin_l_bfgs_b(noisy_logistic_loss, output_vec, fprime=None,
diff --git a/tests/models/test_LogisticRegression.py b/tests/models/test_LogisticRegression.py
index 06d4ba1..b80a208 100644
--- a/tests/models/test_LogisticRegression.py
+++ b/tests/models/test_LogisticRegression.py
@@ -180,7 +180,7 @@ def test_simple(self):
         X -= 3.0
         X /= 2.5
 
-        clf = LogisticRegression(epsilon=2, data_norm=1.0, random_state=0)
+        clf = LogisticRegression(epsilon=2, data_norm=1.0, random_state=1)
         clf.fit(X, y)
 
         self.assertIsNotNone(clf)