diff --git a/opacus/optimizers/ddpoptimizer_fast_gradient_clipping.py b/opacus/optimizers/ddpoptimizer_fast_gradient_clipping.py
index b604911f..dd2c1b94 100644
--- a/opacus/optimizers/ddpoptimizer_fast_gradient_clipping.py
+++ b/opacus/optimizers/ddpoptimizer_fast_gradient_clipping.py
@@ -24,7 +24,7 @@
 
 class DistributedDPOptimizerFastGradientClipping(DPOptimizerFastGradientClipping):
     """
-    :class:`~opacus.optimizers.optimizer.DPOptimizer` compatible with
+    :class:`opacus.optimizers.optimizer.DPOptimizer` compatible with
     distributed data processing
     """
 
diff --git a/opacus/tests/grad_sample_module_fast_gradient_clipping_test.py b/opacus/tests/grad_sample_module_fast_gradient_clipping_test.py
index 819a1649..f46a7a65 100644
--- a/opacus/tests/grad_sample_module_fast_gradient_clipping_test.py
+++ b/opacus/tests/grad_sample_module_fast_gradient_clipping_test.py
@@ -23,6 +23,7 @@
 from opacus.grad_sample import GradSampleModule, GradSampleModuleFastGradientClipping
 from opacus.optimizers import DPOptimizer, DPOptimizerFastGradientClipping
 from opacus.utils.per_sample_gradients_utils import clone_module
+from opacus.utils.fast_gradient_clipping_utils import double_backward
 from torch.utils.data import DataLoader, Dataset
 
 from .grad_sample_module_test import GradSampleModuleTest, SampleConvNet
@@ -108,7 +109,7 @@ def setUp_data_sequantial(self, size, length, dim):
     @settings(deadline=1000000)
     def test_norm_calculation_fast_gradient_clipping(self, size, length, dim):
         """
-        Tests if norm calculation is same between standard (opacus) and fast gradient clipping"
+        Tests if norm calculation is the same between standard (opacus) and fast gradient clipping"
         """
         self.length = length
         self.size = size
@@ -189,7 +190,7 @@ def test_norm_calculation_fast_gradient_clipping(self, size, length, dim):
     @settings(deadline=1000000)
     def test_gradient_calculation_fast_gradient_clipping(self, size, length, dim):
         """
-        Tests if gradients are same between standard (opacus) and fast gradient clipping"
+        Tests if gradients are the same between standard (opacus) and fast gradient clipping, using double_backward function"
         """
 
         noise_multiplier = 0.0
@@ -237,19 +238,10 @@ def test_gradient_calculation_fast_gradient_clipping(self, size, length, dim):
         ]
         flat_grads_normal = torch.cat([p.flatten() for p in all_grads_normal])
 
-        self.grad_sample_module.enable_hooks()
         output_gc = self.grad_sample_module(input_data)
 
         first_loss_per_sample = self.criterion(output_gc, target_data)
-        first_loss = torch.mean(first_loss_per_sample)
-        first_loss.backward(retain_graph=True)
-
-        optimizer_gc.zero_grad()
-        coeff = self.grad_sample_module.get_coeff()
-        second_loss_per_sample = coeff * first_loss_per_sample
-        second_loss = torch.sum(second_loss_per_sample)
-        self.grad_sample_module.disable_hooks()
-        second_loss.backward()
+        double_backward(self.grad_sample_module, optimizer_gc, first_loss_per_sample)
 
         all_grads_gc = [param.grad for param in self.grad_sample_module.parameters()]
         flat_grads_gc = torch.cat([p.flatten() for p in all_grads_gc])
@@ -261,5 +253,5 @@ def test_gradient_calculation_fast_gradient_clipping(self, size, length, dim):
             ]
         )
         logging.info(f"Diff = {diff}")
-        msg = "FAIL: Gradients from vanilla DP-SGD and from fast gradient clipping are different"
+        msg = "Fail: Gradients from vanilla DP-SGD and from fast gradient clipping are different"
         assert torch.allclose(flat_grads_normal, flat_grads_gc, atol=1e-3), msg
diff --git a/opacus/utils/fast_gradient_clipping_utils.py b/opacus/utils/fast_gradient_clipping_utils.py
new file mode 100644
index 00000000..61a3d2be
--- /dev/null
+++ b/opacus/utils/fast_gradient_clipping_utils.py
@@ -0,0 +1,46 @@
+#!/usr/bin/env python3
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import torch
+from opacus.grad_sample.grad_sample_module_fast_gradient_clipping import (
+    GradSampleModuleFastGradientClipping,
+)
+from opacus.optimizers import DPOptimizerFastGradientClipping
+
+
+def double_backward(
+    module: GradSampleModuleFastGradientClipping,
+    optimizer: DPOptimizerFastGradientClipping,
+    loss_per_sample: torch.Tensor,
+) -> None:
+    """
+    Packages the training loop for Fast Gradient and Ghost Clipping. It does the two backward passes, as well as the loss rescaling and hook operations in between.
+
+    Args:
+        module: The DP gradient sample module to train
+        optimizer: The DP optimizer used to train the module
+        loss_per_sample: loss on each sample in the mini-batch of size [batch_size, 1]
+
+    Returns:
+        None
+    """
+
+    torch.mean(loss_per_sample).backward(retain_graph=True)
+    optimizer.zero_grad()
+    rescaled_loss_per_sample = module.get_coeff() * loss_per_sample
+    rescaled_loss = torch.sum(rescaled_loss_per_sample)
+    module.disable_hooks()
+    rescaled_loss.backward()
+    module.enable_hooks()