diff --git a/tensorflow_privacy/privacy/analysis/compute_noise_from_budget.py b/tensorflow_privacy/privacy/analysis/compute_noise_from_budget.py
index 6ae991d..bb23eea 100644
--- a/tensorflow_privacy/privacy/analysis/compute_noise_from_budget.py
+++ b/tensorflow_privacy/privacy/analysis/compute_noise_from_budget.py
@@ -18,12 +18,13 @@ The script applies the RDP accountant to estimate privacy budget of an iterated
 Sampled Gaussian Mechanism. The mechanism's parameters are controlled by flags.
 
 Example:
-  compute_dp_sgd_privacy
+  compute_noise_from_budget
     --N=60000 \
     --batch_size=256 \
     --epsilon=2.92 \
     --epochs=60 \
-    --delta=1e-5
+    --delta=1e-5 \
+    --min_noise=1e-6
 
 The output states that DP-SGD with these parameters should
 use a noise multiplier of 1.12.
@@ -50,6 +51,7 @@ flags.DEFINE_integer('batch_size', None, 'Batch size')
 flags.DEFINE_float('epsilon', None, 'Target epsilon for DP-SGD')
 flags.DEFINE_float('epochs', None, 'Number of epochs (may be fractional)')
 flags.DEFINE_float('delta', 1e-6, 'Target delta')
+flags.DEFINE_float('min_noise', 1e-5, 'Minimum noise level for search.')
 
 
 def main(argv):
@@ -60,7 +62,7 @@ def main(argv):
   assert FLAGS.epsilon is not None, 'Flag epsilon is missing.'
   assert FLAGS.epochs is not None, 'Flag epochs is missing.'
   compute_noise(FLAGS.N, FLAGS.batch_size, FLAGS.epsilon,
-                FLAGS.epochs, FLAGS.delta)
+                FLAGS.epochs, FLAGS.delta, FLAGS.min_noise)
 
 
 if __name__ == '__main__':
diff --git a/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_lib.py b/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_lib.py
index 1d8b107..96032f2 100644
--- a/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_lib.py
+++ b/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_lib.py
@@ -45,7 +45,7 @@ def apply_dp_sgd_analysis(q, sigma, steps, orders, delta):
   return eps, opt_order
 
 
-def compute_noise(n, batch_size, target_epsilon, epochs, delta):
+def compute_noise(n, batch_size, target_epsilon, epochs, delta, noise_lbd):
   """Compute noise based on the given hyperparameters."""
   q = batch_size / n  # q - the sampling ratio.
   if q > 1:
@@ -54,10 +54,11 @@ def compute_noise(n, batch_size, target_epsilon, epochs, delta):
             list(range(5, 64)) + [128, 256, 512])
   steps = int(math.ceil(epochs * n / batch_size))
 
-  init_noise = 1e-5  # minimum possible noise
+  init_noise = noise_lbd  # minimum possible noise
   init_epsilon, _ = apply_dp_sgd_analysis(q, init_noise, steps, orders, delta)
 
-  if init_epsilon < target_epsilon:  # 1e-5 was an overestimate
+  if init_epsilon < target_epsilon:  # noise_lbd was an overestimate
+    print("min_noise too large for target epsilon.")
     return 0
 
   cur_epsilon = init_epsilon
diff --git a/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_test.py b/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_test.py
index f2dd635..c8a5a98 100644
--- a/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_test.py
+++ b/tensorflow_privacy/privacy/analysis/compute_noise_from_budget_test.py
@@ -26,14 +26,15 @@ from tensorflow_privacy.privacy.analysis import compute_noise_from_budget_lib
 class ComputeNoiseFromBudgetTest(parameterized.TestCase):
 
   @parameterized.named_parameters(
-      ('Test0', 60000, 150, 0.941870567, 15, 1e-5, 1.3),
-      ('Test1', 100000, 100, 1.70928734, 30, 1e-7, 1.0),
-      ('Test2', 100000000, 1024, 5907984.81339406, 10, 1e-7, 0.1),
+      ('Test0', 60000, 150, 0.941870567, 15, 1e-5, 1e-5, 1.3),
+      ('Test1', 100000, 100, 1.70928734, 30, 1e-7, 1e-6, 1.0),
+      ('Test2', 100000000, 1024, 5907984.81339406, 10, 1e-7, 1e-5, 0.1),
+      ('Test3', 100000000, 1024, 5907984.81339406, 10, 1e-7, 1, 0),
   )
   def test_compute_noise(self, n, batch_size, target_epsilon, epochs,
-                         delta, expected_noise):
+                         delta, min_noise, expected_noise):
     target_noise = compute_noise_from_budget_lib.compute_noise(
-        n, batch_size, target_epsilon, epochs, delta)
+        n, batch_size, target_epsilon, epochs, delta, min_noise)
     self.assertAlmostEqual(target_noise, expected_noise)
 
 if __name__ == '__main__':