diff --git a/.kokoro b/.kokoro
index 8d0dff6..d820c6d 100755
--- a/.kokoro
+++ b/.kokoro
@@ -1,4 +1,18 @@
 #!/bin/bash
+#
+# Copyright 2017-present The Material Motion Authors. All Rights Reserved.
+#
+# 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.
 
 # Fail on any error.
 set -e
@@ -6,30 +20,36 @@ set -e
 # Display commands to stderr.
 set -x
 
+KOKORO_RUNNER_VERSION="v3.*"
+
+fix_bazel_imports() {
+  if [ -z "$KOKORO_BUILD_NUMBER" ]; then
+    repo_prefix=""
+  else
+    repo_prefix="github/repo/"
+  fi
+
+  # Fixes a bug in bazel where objc_library targets have a _ prefix.
+  find "${repo_prefix}tests/unit" -type f -name '*.swift' -exec sed -i '' -E "s/import Motion(.+)/import _Motion\1/" {} + || true
+  stashed_dir=$(pwd)
+  reset_imports() {
+    # Undoes our source changes from above.
+    find "${stashed_dir}/${tests_dir_prefix}tests/unit" -type f -name '*.swift' -exec sed -i '' -E "s/import _Motion(.+)/import Motion\1/" {} + || true
+  }
+  trap reset_imports EXIT
+}
+
 if [ ! -d .kokoro-ios-runner ]; then
   git clone https://github.com/material-foundation/kokoro-ios-runner.git .kokoro-ios-runner
 fi
 
 pushd .kokoro-ios-runner
 git fetch > /dev/null
-TAG=$(git tag -l "v3*" | sort | tail -n1)
-git checkout $TAG > /dev/null
+TAG=$(git tag --sort=v:refname -l "$KOKORO_RUNNER_VERSION" | tail -n1)
+git checkout "$TAG" > /dev/null
 popd
 
-if [ -z "$KOKORO_BUILD_NUMBER" ]; then
-  tests_dir_prefix=""
-else
-  tests_dir_prefix="github/repo/"
-fi
-
-# Fixes a bug in bazel where objc_library targets have a _ prefix.
-find ${tests_dir_prefix}tests/unit -type f -name '*.swift' -exec sed -i '' -E "s/import Motion(.+)/import _Motion\1/" {} + || true
-stashed_dir=$(pwd)
-reset_imports() {
-  # Undoes our source changes from above.
-  find ${stashed_dir}/${tests_dir_prefix}tests/unit -type f -name '*.swift' -exec sed -i '' -E "s/import _Motion(.+)/import Motion\1/" {} + || true
-}
-trap reset_imports EXIT
+fix_bazel_imports
 
 ./.kokoro-ios-runner/bazel.sh test //:UnitTests 8.1.0
 
diff --git a/BUILD b/BUILD
index 4ade595..c77a8fc 100644
--- a/BUILD
+++ b/BUILD
@@ -1,3 +1,17 @@
+# Copyright 2017-present The Material Motion Authors. All Rights Reserved.
+#
+# 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.
+#
 # Description:
 # Light-weight API for building UIViewController transitions.
 
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2e5aaf1..406f7fe 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,16 @@
+# 4.0.2
+
+This patch release fixes a bug where the frames of custom presented views would be incorrectly set
+to the view controller's frame.
+
+## Source changes
+
+* [Add support for transitions with custom presented views. (#55)](https://github.com/material-motion/motion-transitioning-objc/commit/2564bfdf42a2ba7c550656b95bc7dc98019468bb) (featherless)
+
+## Non-source changes
+
+* [Standardize the kokoro and bazel files. (#51)](https://github.com/material-motion/motion-transitioning-objc/commit/588b63dfae7471f3377041caa08496ef1fa74ced) (featherless)
+
 # 4.0.1
 
 This patch release resolves a build warning and migrates the project's continuous integration to
diff --git a/MotionTransitioning.podspec b/MotionTransitioning.podspec
index cde300b..17bda58 100644
--- a/MotionTransitioning.podspec
+++ b/MotionTransitioning.podspec
@@ -1,7 +1,7 @@
 Pod::Spec.new do |s|
   s.name         = "MotionTransitioning"
   s.summary      = "Light-weight API for building UIViewController transitions."
-  s.version      = "4.0.1"
+  s.version      = "4.0.2"
   s.authors      = "The Material Motion Authors"
   s.license      = "Apache 2.0"
   s.homepage     = "https://github.com/material-motion/transitioning-objc"
diff --git a/Podfile.lock b/Podfile.lock
index 28cf967..c4f0389 100644
--- a/Podfile.lock
+++ b/Podfile.lock
@@ -1,6 +1,6 @@
 PODS:
   - CatalogByConvention (2.1.1)
-  - MotionTransitioning (4.0.1)
+  - MotionTransitioning (4.0.2)
 
 DEPENDENCIES:
   - CatalogByConvention
@@ -12,7 +12,7 @@ EXTERNAL SOURCES:
 
 SPEC CHECKSUMS:
   CatalogByConvention: c3a5319de04250a7cd4649127fcfca5fe3322a43
-  MotionTransitioning: 277501a1a1e6121c0ab523e6a3e00d64659c3367
+  MotionTransitioning: 9885e68bd1501f1f8244b2e40081acd8cf3ac461
 
 PODFILE CHECKSUM: 25d5942fb7698339a03667bb46c3fbb77529b92d
 
diff --git a/WORKSPACE b/WORKSPACE
index c01a93d..722a7a4 100644
--- a/WORKSPACE
+++ b/WORKSPACE
@@ -1,3 +1,17 @@
+# Copyright 2017-present The Material Motion Authors. All Rights Reserved.
+#
+# 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.
+
 git_repository(
     name = "build_bazel_rules_apple",
     remote = "https://github.com/bazelbuild/rules_apple.git",
@@ -7,5 +21,5 @@ git_repository(
 git_repository(
     name = "bazel_ios_warnings",
     remote = "https://github.com/material-foundation/bazel_ios_warnings.git",
-    commit = "3e61cb5b60f52c8b9c77b5d62364d8b4d25e528f",
+    tag = "v1.0.1",
 )
diff --git a/src/private/MDMViewControllerTransitionCoordinator.m b/src/private/MDMViewControllerTransitionCoordinator.m
index 9dd1e8f..4da369e 100644
--- a/src/private/MDMViewControllerTransitionCoordinator.m
+++ b/src/private/MDMViewControllerTransitionCoordinator.m
@@ -313,35 +313,43 @@ - (void)initiateTransition {
   _root.transitionContext = _transitionContext;
 
   UIViewController *from = [_transitionContext viewControllerForKey:UITransitionContextFromViewControllerKey];
-  if (from) {
+  UIView *fromView = [_transitionContext viewForKey:UITransitionContextFromViewKey];
+  if (fromView == nil) {
+    fromView = from.view;
+  }
+  if (fromView != nil && fromView == from.view) {
     CGRect finalFrame = [_transitionContext finalFrameForViewController:from];
     if (!CGRectIsEmpty(finalFrame)) {
-      from.view.frame = finalFrame;
+      fromView.frame = finalFrame;
     }
   }
 
   UIViewController *to = [_transitionContext viewControllerForKey:UITransitionContextToViewControllerKey];
-  if (to) {
+  UIView *toView = [_transitionContext viewForKey:UITransitionContextToViewKey];
+  if (toView == nil) {
+    toView = to.view;
+  }
+  if (toView != nil && toView == to.view) {
     CGRect finalFrame = [_transitionContext finalFrameForViewController:to];
     if (!CGRectIsEmpty(finalFrame)) {
-      to.view.frame = finalFrame;
+      toView.frame = finalFrame;
     }
 
-    switch (_direction) {
-      case MDMTransitionDirectionForward:
-        [_transitionContext.containerView addSubview:to.view];
-        break;
+    if (toView.superview == nil) {
+      switch (_direction) {
+        case MDMTransitionDirectionForward:
+          [_transitionContext.containerView addSubview:toView];
+          break;
 
-      case MDMTransitionDirectionBackward:
-        if (!to.view.superview) {
-          [_transitionContext.containerView insertSubview:to.view atIndex:0];
-        }
-        break;
+        case MDMTransitionDirectionBackward:
+          [_transitionContext.containerView insertSubview:toView atIndex:0];
+          break;
+      }
     }
-
-    [to.view layoutIfNeeded];
   }
 
+  [toView layoutIfNeeded];
+
   [_root attemptFallback];
   [self anticipateOnlyExplicitAnimations];