diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 915cd3f..30f1fe5 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -47,5 +47,28 @@ jobs:
       - name: Check build-logic
         run: ./gradlew -p build-logic ktfmtCheck checkSortDependencies detekt
 
+      # `build` overlaps the Gradle and Kotlin daemons, Kotlin/Native, R8, webpack and karma's
+      # Chrome, and peaks above the runner's 16 GB. When it does, the runner itself is OOM-killed
+      # and the job ends as "The operation was canceled" with no Gradle error. The image ships a
+      # 4 GB swapfile; a larger one lets the peak page out instead.
+      - name: Enlarge swap
+        run: |
+          sudo swapoff -a
+          sudo rm -f /mnt/swapfile
+          sudo fallocate -l 12G /mnt/swapfile
+          sudo chmod 600 /mnt/swapfile
+          sudo mkswap /mnt/swapfile
+          sudo swapon /mnt/swapfile
+          free -h
+
+      # The sampler prints into this step's own log so the numbers survive the runner being
+      # killed; a file or a later step would not.
       - name: Build
-        run: ./gradlew build
+        run: |
+          ( while sleep 30; do
+              echo "::group::resources $(date -u +%T)"
+              free -m; df -h / /mnt
+              ps -eo rss:10,args --sort=-rss | head -8 | cut -c1-160
+              echo "::endgroup::"
+            done ) &
+          ./gradlew build
diff --git a/build.gradle.kts b/build.gradle.kts
index 7fb9912..cd5cfc6 100644
--- a/build.gradle.kts
+++ b/build.gradle.kts
@@ -1,5 +1,7 @@
 import com.ncorti.ktfmt.gradle.KtfmtExtension
 import org.gradle.buildconfiguration.tasks.UpdateDaemonJvm
+import org.jetbrains.kotlin.gradle.targets.js.testing.KotlinJsTest
+import org.jetbrains.kotlin.gradle.targets.js.webpack.KotlinWebpack
 
 // AGP 9.x has built-in Kotlin support, pinned to an older Kotlin Gradle Plugin (KGP) version.
 // Metro 1.3.2 needs Kotlin >= 2.3.20 and Compose needs a matching compiler plugin, so we override
@@ -29,3 +31,21 @@ tasks.named<UpdateDaemonJvm>("updateDaemonJvm") {
     languageVersion = JavaLanguageVersion.of(25)
     vendor.set(JvmVendorSpec.AMAZON)
 }
+
+// On CI, run the webpack and karma tasks one at a time. Each starts a Node process sized for a
+// whole Compose bundle, and karma adds a Chrome on top. `build` has seven modules with web
+// executables, so under org.gradle.parallel they overlap alongside the Gradle and Kotlin daemons,
+// exhaust ubuntu-latest's 16 GB, and the runner is killed: the job ends as "The operation was
+// canceled" or "The runner has received a shutdown signal", with no Gradle error at all.
+// Locally there is enough memory, so they stay parallel.
+abstract class WebBundleTaskLimiter : BuildService<BuildServiceParameters.None>
+
+val webBundleTaskLimiter =
+    gradle.sharedServices.registerIfAbsent("webBundleTaskLimiter", WebBundleTaskLimiter::class) {
+        if (providers.environmentVariable("CI").isPresent) maxParallelUsages = 1
+    }
+
+subprojects {
+    tasks.withType<KotlinWebpack>().configureEach { usesService(webBundleTaskLimiter) }
+    tasks.withType<KotlinJsTest>().configureEach { usesService(webBundleTaskLimiter) }
+}