diff --git a/src/george/modeling.py b/src/george/modeling.py
index 6fe441b6..44a48ed5 100644
--- a/src/george/modeling.py
+++ b/src/george/modeling.py
@@ -115,15 +115,15 @@ def compute_gradient(self, *args, **kwargs):
 
         """
         _EPS = 1.254e-5
-        vector = self.get_parameter_vector()
+        vector = self.get_parameter_vector(include_frozen=True)
         value0 = self.get_value(*args, **kwargs)
         grad = np.empty([len(vector)] + list(value0.shape), dtype=np.float64)
         for i, v in enumerate(vector):
             vector[i] = v + _EPS
-            self.set_parameter_vector(vector)
+            self.set_parameter_vector(vector, include_frozen=True)
             value = self.get_value(*args, **kwargs)
             vector[i] = v
-            self.set_parameter_vector(vector)
+            self.set_parameter_vector(vector, include_frozen=True)
             grad[i] = (value - value0) / _EPS
         return grad
 
diff --git a/tests/test_modeling.py b/tests/test_modeling.py
index 050871ce..43457bbb 100644
--- a/tests/test_modeling.py
+++ b/tests/test_modeling.py
@@ -72,6 +72,13 @@ def compute_gradient(self, x):
         return dict(m=x, b=np.ones(len(x)))
 
 
+class LinearWhiteNoiseWithoutGrad(Model):
+    parameter_names = ("m", "b")
+
+    def get_value(self, x):
+        return self.m * x + self.b
+
+
 def test_gp_callable_white_noise(N=50, seed=1234):
     np.random.seed(seed)
     x = np.random.uniform(0, 5)
@@ -86,6 +93,20 @@ def test_gp_callable_white_noise(N=50, seed=1234):
     check_gradient(gp, y)
 
 
+def test_gp_callable_white_noise_without_grad(N=50, seed=1234):
+    np.random.seed(seed)
+    x = np.random.uniform(0, 5)
+    y = 5 + np.sin(x)
+    gp = GP(10. * kernels.ExpSquaredKernel(1.3), mean=5.0,
+            white_noise=LinearWhiteNoiseWithoutGrad(-6, 0.01),
+            fit_white_noise=True)
+    gp.compute(x)
+    check_gradient(gp, y)
+
+    gp.freeze_parameter("white_noise:m")
+    check_gradient(gp, y)
+
+
 def test_parameters():
     kernel = 10 * kernels.ExpSquaredKernel(1.0)
     kernel += 0.5 * kernels.RationalQuadraticKernel(log_alpha=0.1, metric=5.0)