diff --git a/test/jdk/java/lang/Thread/virtual/ThreadAPI.java b/test/jdk/java/lang/Thread/virtual/ThreadAPI.java
index 0cf2bd8531b..9476694473f 100644
--- a/test/jdk/java/lang/Thread/virtual/ThreadAPI.java
+++ b/test/jdk/java/lang/Thread/virtual/ThreadAPI.java
@@ -754,7 +754,7 @@ public class ThreadAPI {
 
     /**
      * Test platform thread invoking timed-Thread.join on a thread that is parking
-     * and unparking.
+     * and unparking while pinned.
      */
     @Test
     public void testJoin33() throws Exception {
@@ -775,11 +775,18 @@ public class ThreadAPI {
 
     /**
      * Test virtual thread invoking timed-Thread.join on a thread that is parking
-     * and unparking.
+     * and unparking while pinned.
      */
     @Test
     public void testJoin34() throws Exception {
-        VThreadRunner.run(this::testJoin33);
+        // need at least two carrier threads due to pinning
+        int previousParallelism = VThreadRunner.ensureParallelism(2);
+        try {
+            VThreadRunner.run(this::testJoin33);
+        } finally {
+            // restore
+            VThreadRunner.setParallelism(previousParallelism);
+        }
     }
 
     /**
diff --git a/test/jdk/java/lang/management/ThreadMXBean/VirtualThreadDeadlocks.java b/test/jdk/java/lang/management/ThreadMXBean/VirtualThreadDeadlocks.java
index bfaed07494c..52ef8dd4375 100644
--- a/test/jdk/java/lang/management/ThreadMXBean/VirtualThreadDeadlocks.java
+++ b/test/jdk/java/lang/management/ThreadMXBean/VirtualThreadDeadlocks.java
@@ -22,22 +22,24 @@
  */
 
 /**
- * @test
+ * @test id=default
  * @bug 8284161 8287103
  * @summary Test ThredMXBean.findMonitorDeadlockedThreads with cycles of
  *   platform and virtual threads in deadlock
  * @enablePreview
- * @modules java.management
+ * @modules java.base/java.lang:+open java.management
+ * @library /test/lib
  * @run main/othervm VirtualThreadDeadlocks PP
  * @run main/othervm VirtualThreadDeadlocks PV
  * @run main/othervm VirtualThreadDeadlocks VV
  */
 
 /**
- * @test
+ * @test id=no-vmcontinuations
  * @requires vm.continuations
  * @enablePreview
- * @modules java.management
+ * @modules java.base/java.lang:+open java.management
+ * @library /test/lib
  * @run main/othervm -XX:+UnlockExperimentalVMOptions -XX:-VMContinuations VirtualThreadDeadlocks PP
  * @run main/othervm -XX:+UnlockExperimentalVMOptions -XX:-VMContinuations VirtualThreadDeadlocks PV
  * @run main/othervm -XX:+UnlockExperimentalVMOptions -XX:-VMContinuations VirtualThreadDeadlocks VV
@@ -48,6 +50,7 @@ import java.lang.management.ThreadMXBean;
 import java.util.Arrays;
 import java.util.concurrent.CyclicBarrier;
 import java.util.stream.Stream;
+import jdk.test.lib.thread.VThreadRunner;
 
 public class VirtualThreadDeadlocks {
     private static final Object LOCK1 = new Object();
@@ -61,6 +64,8 @@ public class VirtualThreadDeadlocks {
      * VV = test deadlock with two virtual threads
      */
     public static void main(String[] args) throws Exception {
+        // need at least two carrier threads due to pinning
+        VThreadRunner.ensureParallelism(2);
 
         // start thread1
         Thread.Builder builder1 = (args[0].charAt(0) == 'P')
diff --git a/test/jdk/java/lang/management/ThreadMXBean/VirtualThreads.java b/test/jdk/java/lang/management/ThreadMXBean/VirtualThreads.java
index b986a8cab4f..eff2b62ffae 100644
--- a/test/jdk/java/lang/management/ThreadMXBean/VirtualThreads.java
+++ b/test/jdk/java/lang/management/ThreadMXBean/VirtualThreads.java
@@ -22,7 +22,7 @@
  */
 
 /**
- * @test
+ * @test id=default
  * @bug 8284161 8290562
  * @summary Test java.lang.management.ThreadMXBean with virtual threads
  * @enablePreview
@@ -31,7 +31,7 @@
  */
 
 /**
- * @test
+ * @test id=no-vmcontinuations
  * @requires vm.continuations
  * @enablePreview
  * @modules java.base/java.lang:+open java.management
diff --git a/test/lib/jdk/test/lib/thread/VThreadRunner.java b/test/lib/jdk/test/lib/thread/VThreadRunner.java
index adacfe0b9b5..106739ee7ab 100644
--- a/test/lib/jdk/test/lib/thread/VThreadRunner.java
+++ b/test/lib/jdk/test/lib/thread/VThreadRunner.java
@@ -23,11 +23,13 @@
 
 package jdk.test.lib.thread;
 
+import java.lang.reflect.Field;
 import java.time.Duration;
+import java.util.concurrent.ForkJoinPool;
 import java.util.concurrent.atomic.AtomicReference;
 
 /**
- * Helper class for running tasks in a virtual thread.
+ * Helper class to support tests running tasks a in virtual thread.
  */
 public class VThreadRunner {
     private VThreadRunner() { }
@@ -140,4 +142,41 @@ public class VThreadRunner {
     public static void run(ThrowingRunnable task) throws Exception {
         run(null, 0, task);
     }
+
+    /**
+     * Returns the virtual thread scheduler.
+     */
+    private static ForkJoinPool defaultScheduler() {
+        try {
+            var clazz = Class.forName("java.lang.VirtualThread");
+            var field = clazz.getDeclaredField("DEFAULT_SCHEDULER");
+            field.setAccessible(true);
+            return (ForkJoinPool) field.get(null);
+        } catch (Exception e) {
+            throw new RuntimeException(e);
+        }
+    }
+
+    /**
+     * Sets the virtual thread scheduler's target parallelism.
+     * @return the previous parallelism level
+     */
+    public static int setParallelism(int size) {
+        return defaultScheduler().setParallelism(size);
+    }
+
+    /**
+     * Ensures that the virtual thread scheduler's target parallelism is at least
+     * the given size. If the target parallelism is less than the given size then
+     * it is changed to the given size.
+     * @return the previous parallelism level
+     */
+    public static int ensureParallelism(int size) {
+        ForkJoinPool pool = defaultScheduler();
+        int parallelism = pool.getParallelism();
+        if (size > parallelism) {
+            pool.setParallelism(size);
+        }
+        return parallelism;
+    }
 }