diff --git a/tests/run-tests.py b/tests/run-tests.py
index e5d7123036..bbc98cad96 100755
--- a/tests/run-tests.py
+++ b/tests/run-tests.py
@@ -562,13 +562,19 @@ def run_tests(pyb, tests, args, result_dir, num_threads=1):
         skip_tests.add("cmdline/repl_sys_ps1_ps2.py")
         skip_tests.add("extmod/ssl_poll.py")
 
-    # Some tests shouldn't be run on a PC
-    if args.target == "unix":
-        # unix build does not have the GIL so can't run thread mutation tests
+    # Skip thread mutation tests on targets that don't have the GIL.
+    if args.target in ("rp2", "unix"):
         for t in tests:
             if t.startswith("thread/mutate_"):
                 skip_tests.add(t)
 
+    # Skip thread tests that require many threads on targets that don't support multiple threads.
+    if args.target == "rp2":
+        skip_tests.add("thread/stress_heap.py")
+        skip_tests.add("thread/thread_lock2.py")
+        skip_tests.add("thread/thread_lock3.py")
+        skip_tests.add("thread/thread_shared2.py")
+
     # Some tests shouldn't be run on pyboard
     if args.target != "unix":
         skip_tests.add("basics/exception_chain.py")  # warning is not printed
@@ -987,7 +993,7 @@ the last matching regex is used:
             elif args.target in ("renesas-ra"):
                 test_dirs += ("float", "inlineasm", "renesas-ra")
             elif args.target == "rp2":
-                test_dirs += ("float", "stress", "inlineasm")
+                test_dirs += ("float", "stress", "inlineasm", "thread")
             elif args.target in ("esp8266", "esp32", "minimal", "nrf"):
                 test_dirs += ("float",)
             elif args.target == "wipy":
diff --git a/tests/thread/stress_schedule.py b/tests/thread/stress_schedule.py
index 40191e6620..a5d7dc824e 100644
--- a/tests/thread/stress_schedule.py
+++ b/tests/thread/stress_schedule.py
@@ -19,6 +19,7 @@ _TIMEOUT_MS = 10000
 
 n = 0  # How many times the task successfully ran.
 t = None  # Start time of test, assigned here to preallocate entry in globals dict.
+thread_run = True  # If the thread should continue running.
 
 
 def task(x):
@@ -27,7 +28,7 @@ def task(x):
 
 
 def thread():
-    while True:
+    while thread_run:
         try:
             micropython.schedule(task, None)
         except RuntimeError:
@@ -36,13 +37,21 @@ def thread():
 
 
 for i in range(8):
-    _thread.start_new_thread(thread, ())
+    try:
+        _thread.start_new_thread(thread, ())
+    except OSError:
+        # System cannot create a new thead, so stop trying to create them.
+        break
 
 # Wait up to 10 seconds for 10000 tasks to be scheduled.
 t = time.ticks_ms()
 while n < _NUM_TASKS and time.ticks_diff(time.ticks_ms(), t) < _TIMEOUT_MS:
     pass
 
+# Stop all threads.
+thread_run = False
+time.sleep_ms(20)
+
 if n < _NUM_TASKS:
     # Not all the tasks were scheduled, likely the scheduler stopped working.
     print(n)
diff --git a/tests/thread/thread_gc1.py b/tests/thread/thread_gc1.py
index dd1e64d894..b36ea9d4c8 100644
--- a/tests/thread/thread_gc1.py
+++ b/tests/thread/thread_gc1.py
@@ -16,21 +16,34 @@ def thread_entry(n):
             data[i] = data[i]
         gc.collect()
 
-    # print whether the data remains intact and indicate we are finished
+    # check whether the data remains intact and indicate we are finished
     with lock:
-        print(list(data) == list(range(256)))
-        global n_finished
+        global n_correct, n_finished
+        n_correct += list(data) == list(range(256))
         n_finished += 1
 
 
 lock = _thread.allocate_lock()
-n_thread = 4
+n_thread = 0
+n_thread_max = 4
+n_correct = 0
 n_finished = 0
 
 # spawn threads
-for i in range(n_thread):
-    _thread.start_new_thread(thread_entry, (10,))
+for _ in range(n_thread_max):
+    try:
+        _thread.start_new_thread(thread_entry, (10,))
+        n_thread += 1
+    except OSError:
+        # System cannot create a new thead, so stop trying to create them.
+        break
+
+# also run the function on this main thread
+thread_entry(10)
+n_thread += 1
 
 # busy wait for threads to finish
 while n_finished < n_thread:
     pass
+
+print(n_correct == n_finished)
diff --git a/tests/thread/thread_ident1.py b/tests/thread/thread_ident1.py
index 8e106cd317..2a3732eff5 100644
--- a/tests/thread/thread_ident1.py
+++ b/tests/thread/thread_ident1.py
@@ -5,7 +5,12 @@
 import _thread
 
 
+# Initialise variables (also preallocate their spot in the globals dict so the
+# globals dict is not resized while threads are running).
 tid = None
+tid_main = None
+new_tid = None
+finished = False
 
 
 def thread_entry():
@@ -19,7 +24,6 @@ def thread_entry():
 tid_main = _thread.get_ident()
 print("main", type(tid_main) == int, tid_main != 0)
 
-finished = False
 new_tid = _thread.start_new_thread(thread_entry, ())
 
 while not finished:
diff --git a/tests/thread/thread_lock4.py b/tests/thread/thread_lock4.py
index 97c3dc5380..b424ee3d02 100644
--- a/tests/thread/thread_lock4.py
+++ b/tests/thread/thread_lock4.py
@@ -36,14 +36,18 @@ output_lock = _thread.allocate_lock()
 
 # spawn threads to do the jobs
 for i in range(4):
-    _thread.start_new_thread(thread_entry, ())
+    try:
+        _thread.start_new_thread(thread_entry, ())
+    except OSError:
+        # System cannot create a new thead, so stop trying to create them.
+        break
 
 # wait for the jobs to complete
 while True:
     with jobs_lock:
         if len(output) == n_jobs:
             break
-    time.sleep(1)
+    time.sleep(0)
 
 # sort and print the results
 output.sort(key=lambda x: x[0])
diff --git a/tests/thread/thread_qstr1.py b/tests/thread/thread_qstr1.py
index f184d2a58e..96f12c5d8c 100644
--- a/tests/thread/thread_qstr1.py
+++ b/tests/thread/thread_qstr1.py
@@ -24,16 +24,26 @@ def th(base, n):
 
 
 lock = _thread.allocate_lock()
-n_thread = 4
+n_thread = 0
+n_thread_max = 4
 n_finished = 0
 n_qstr_per_thread = 100  # make 1000 for a more stressful test (uses more heap)
 
 # spawn threads
-for i in range(n_thread):
-    _thread.start_new_thread(th, (i * n_qstr_per_thread, n_qstr_per_thread))
+for _ in range(n_thread_max):
+    try:
+        _thread.start_new_thread(th, (n_thread * n_qstr_per_thread, n_qstr_per_thread))
+        n_thread += 1
+    except OSError:
+        # System cannot create a new thead, so stop trying to create them.
+        break
+
+# also run the function on this main thread
+th(n_thread * n_qstr_per_thread, n_qstr_per_thread)
+n_thread += 1
 
 # wait for threads to finish
 while n_finished < n_thread:
-    time.sleep(1)
+    time.sleep(0)
 
 print("pass")
diff --git a/tests/thread/thread_shared1.py b/tests/thread/thread_shared1.py
index 582b01fc34..251e26fae6 100644
--- a/tests/thread/thread_shared1.py
+++ b/tests/thread/thread_shared1.py
@@ -18,15 +18,25 @@ def thread_entry(n, tup):
 
 
 lock = _thread.allocate_lock()
-n_thread = 2
+n_thread = 0
+n_thread_max = 2
 n_finished = 0
 
 # the shared data structure
 tup = (1, 2, 3, 4)
 
 # spawn threads
-for i in range(n_thread):
-    _thread.start_new_thread(thread_entry, (100, tup))
+for _ in range(n_thread_max):
+    try:
+        _thread.start_new_thread(thread_entry, (100, tup))
+        n_thread += 1
+    except OSError:
+        # System cannot create a new thead, so stop trying to create them.
+        break
+
+# also run the function on this main thread
+thread_entry(100, tup)
+n_thread += 1
 
 # busy wait for threads to finish
 while n_finished < n_thread:
diff --git a/tests/thread/thread_sleep1.py b/tests/thread/thread_sleep1.py
index add9b02f15..36f775d1f6 100644
--- a/tests/thread/thread_sleep1.py
+++ b/tests/thread/thread_sleep1.py
@@ -12,7 +12,8 @@ else:
 import _thread
 
 lock = _thread.allocate_lock()
-n_thread = 4
+n_thread = 0
+n_thread_max = 4
 n_finished = 0
 
 
@@ -24,10 +25,20 @@ def thread_entry(t):
         n_finished += 1
 
 
-for i in range(n_thread):
-    _thread.start_new_thread(thread_entry, (10 * i,))
+# spawn threads
+for _ in range(n_thread_max):
+    try:
+        _thread.start_new_thread(thread_entry, (10 * n_thread,))
+        n_thread += 1
+    except OSError:
+        # System cannot create a new thead, so stop trying to create them.
+        break
+
+# also run the function on this main thread
+thread_entry(10 * n_thread)
+n_thread += 1
 
 # wait for threads to finish
 while n_finished < n_thread:
     sleep_ms(100)
-print("done", n_thread)
+print("done")