diff --git a/gradle/core/build.gradle b/gradle/core/build.gradle
index d1c4d03c0..bc64f1105 100644
--- a/gradle/core/build.gradle
+++ b/gradle/core/build.gradle
@@ -41,6 +41,19 @@ def fragileTestPatterns = [
     "google/registry/model/server/KmsSecretRevisionTest.*"
 ]
 
+// Tests that fail when running Gradle in a docker container, e. g. when
+// building the release artifacts in Google Cloud Build.
+def dockerIncompatibleTestPatterns = [
+    // The webdriver tests start headless Chrome in a Docker container,
+    // resulting in Docker-in-Docker complications.
+    "google/registry/webdriver/*",
+    // PathParameterTest includes tests which validate that file permissions are
+    // respected. However when running in Docker the user is root by default, so
+    // every file is read/write-able. There is no way to exclude specific test
+    // methods, so we exclude the whole test class.
+    "google/registry/tools/params/PathParameterTest.*"
+]
+
 sourceSets {
   main {
     java {
@@ -636,6 +649,10 @@ test {
   exclude fragileTestPatterns
   exclude outcastTestPatterns
 
+  if (rootProject.findProperty("skipDockerIncompatibleTests") == "true") {
+    exclude dockerIncompatibleTestPatterns
+  }
+
   // Run every test class in its own process.
   // Uncomment to unblock build while troubleshooting inexplicable test errors.
   // This setting makes the build take 35 minutes, without it it takes about 10.
diff --git a/gradle/gradle/wrapper/gradle-wrapper.properties b/gradle/gradle/wrapper/gradle-wrapper.properties
index 5f1b1201a..f4d7b2bf6 100644
--- a/gradle/gradle/wrapper/gradle-wrapper.properties
+++ b/gradle/gradle/wrapper/gradle-wrapper.properties
@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-5.4-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-5.4.1-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists
diff --git a/release/cloudbuild-nomulus.yaml b/release/cloudbuild-nomulus.yaml
index da2c2cb27..6c3fb2fda 100644
--- a/release/cloudbuild-nomulus.yaml
+++ b/release/cloudbuild-nomulus.yaml
@@ -26,7 +26,7 @@ steps:
   args: ['mkdir', 'nomulus']
 # Run tests
 - name: 'gcr.io/${PROJECT_ID}/builder:latest'
-  args: ['./gradlew', 'test']
+  args: ['./gradlew', 'test', '-PskipDockerIncompatibleTests=true']
   dir: 'gradle'
 # Build and package the deployment files for alpha.
 - name: 'gcr.io/${PROJECT_ID}/builder:latest'