diff --git a/tf_shell_ml/test/dpsgd_conv_model_local_test.py b/tf_shell_ml/test/dpsgd_conv_model_local_test.py
index 6438a34..5df0221 100644
--- a/tf_shell_ml/test/dpsgd_conv_model_local_test.py
+++ b/tf_shell_ml/test/dpsgd_conv_model_local_test.py
@@ -32,6 +32,11 @@ def _test_model(self, disable_encryption, disable_masking, disable_noise, cache)
         x_train, x_test = x_train / np.float32(255.0), x_test / np.float32(255.0)
         y_train, y_test = tf.one_hot(y_train, 10), tf.one_hot(y_test, 10)
 
+        # Clip the input images to make testing faster.
+        clip_by = 8
+        x_train = x_train[:, clip_by : (28 - clip_by), clip_by : (28 - clip_by), :]
+        x_test = x_test[:, clip_by : (28 - clip_by), clip_by : (28 - clip_by), :]
+
         labels_dataset = tf.data.Dataset.from_tensor_slices(y_train)
         labels_dataset = labels_dataset.batch(2**12)
 
@@ -44,7 +49,8 @@ def _test_model(self, disable_encryption, disable_masking, disable_noise, cache)
         m = tf_shell_ml.DpSgdSequential(
             [
                 # Model from tensorflow-privacy tutorial. The first layer may
-                # be skipped and the model still has ~95% accuracy (plaintext).
+                # be skipped and the model still has ~95% accuracy (plaintext,
+                # no input clipping).
                 # tf_shell_ml.Conv2D(
                 #     filters=16,
                 #     kernel_size=8,
@@ -61,7 +67,6 @@ def _test_model(self, disable_encryption, disable_masking, disable_noise, cache)
                     filters=32,
                     kernel_size=4,
                     strides=2,
-                    padding="valid",
                     activation=tf_shell_ml.relu,
                     activation_deriv=tf_shell_ml.relu_deriv,
                 ),
@@ -101,23 +106,23 @@ def _test_model(self, disable_encryption, disable_masking, disable_noise, cache)
 
         m.compile(
             shell_loss=tf_shell_ml.CategoricalCrossentropy(),
-            optimizer=tf.keras.optimizers.Adam(0.1),
+            optimizer=tf.keras.optimizers.Adam(0.18),
             metrics=[tf.keras.metrics.CategoricalAccuracy()],
         )
 
-        m.build([None, 28, 28, 1])
+        m.build([None, 28 - (2 * clip_by), 28 - (2 * clip_by), 1])
         m.summary()
 
         history = m.fit(
             features_dataset,
             labels_dataset,
-            steps_per_epoch=8,
+            steps_per_epoch=1,
             epochs=1,
-            verbose=2,
+            verbose=1,
             validation_data=val_dataset,
         )
 
-        self.assertGreater(history.history["val_categorical_accuracy"][-1], 0.25)
+        self.assertGreater(history.history["val_categorical_accuracy"][-1], 0.13)
 
     def test_model(self):
         with tempfile.TemporaryDirectory() as cache_dir: