diff --git a/winsup/testsuite/winsup.api/pthread/inherit1.c b/winsup/testsuite/winsup.api/pthread/inherit1.c
index 16c3f534b..f036462aa 100644
--- a/winsup/testsuite/winsup.api/pthread/inherit1.c
+++ b/winsup/testsuite/winsup.api/pthread/inherit1.c
@@ -50,6 +50,23 @@ void * func(void * arg)
   return (void *) (size_t)param.sched_priority;
 }
 
+// Windows only supports 7 thread priority levels, which we map onto the 32
+// required by POSIX.  The exact mapping also depends on the overall process
+// priority class. So only a subset of values will be returned exactly by
+// pthread_getschedparam() after pthread_setschedparam().
+int doable_pri(int pri)
+{
+  switch (GetPriorityClass(GetCurrentProcess()))
+    {
+    case BELOW_NORMAL_PRIORITY_CLASS:
+      return (pri == 2) || (pri ==  8) || (pri == 10) || (pri == 12) || (pri == 14) || (pri == 16) || (pri == 30);
+    case NORMAL_PRIORITY_CLASS:
+      return (pri == 2) || (pri == 12) || (pri == 14) || (pri == 16) || (pri == 18) || (pri == 20) || (pri == 30);
+    }
+
+  return TRUE;
+}
+
 int
 main()
 {
@@ -81,7 +98,9 @@ main()
       assert(pthread_setschedparam(mainThread, SCHED_FIFO, &mainParam) == 0);
       assert(pthread_getschedparam(mainThread, &policy, &mainParam) == 0);
       assert(policy == SCHED_FIFO);
-      assert(mainParam.sched_priority == prio);
+
+      if (doable_pri(prio))
+        assert(mainParam.sched_priority == prio);
 
       for (param.sched_priority = prio;
            param.sched_priority <= maxPrio;
diff --git a/winsup/testsuite/winsup.api/pthread/priority1.c b/winsup/testsuite/winsup.api/pthread/priority1.c
index a1e8d051d..135f77d76 100644
--- a/winsup/testsuite/winsup.api/pthread/priority1.c
+++ b/winsup/testsuite/winsup.api/pthread/priority1.c
@@ -50,7 +50,24 @@ void * func(void * arg)
   assert(policy == SCHED_FIFO);
   return (void *)(size_t)param.sched_priority;
 }
- 
+
+// Windows only supports 7 thread priority levels, which we map onto the 32
+// required by POSIX.  The exact mapping also depends on the overall process
+// priority class. So only a subset of values will be returned exactly by
+// pthread_getschedparam() after pthread_setschedparam().
+int doable_pri(int pri)
+{
+  switch (GetPriorityClass(GetCurrentProcess()))
+    {
+    case BELOW_NORMAL_PRIORITY_CLASS:
+      return (pri == 2) || (pri ==  8) || (pri == 10) || (pri == 12) || (pri == 14) || (pri == 16) || (pri == 30);
+    case NORMAL_PRIORITY_CLASS:
+      return (pri == 2) || (pri == 12) || (pri == 14) || (pri == 16) || (pri == 18) || (pri == 20) || (pri == 30);
+    }
+
+  return TRUE;
+}
+
 int
 main()
 {
@@ -61,6 +78,8 @@ main()
   int maxPrio = sched_get_priority_max(SCHED_FIFO);
   int minPrio = sched_get_priority_min(SCHED_FIFO);
 
+  assert((maxPrio - minPrio) >= 31);
+
   assert(pthread_attr_init(&attr) == 0);
   assert(pthread_attr_setinheritsched(&attr, PTHREAD_EXPLICIT_SCHED) == 0);
 
@@ -71,7 +90,8 @@ main()
       assert(pthread_attr_setschedparam(&attr, &param) == 0);
       assert(pthread_create(&t, &attr, func, NULL) == 0);
       pthread_join(t, &result);
-      assert((int)(size_t) result == param.sched_priority);
+      if (doable_pri(param.sched_priority))
+	assert((int)(size_t) result == param.sched_priority);
     }
 
   return 0;
diff --git a/winsup/testsuite/winsup.api/pthread/priority2.c b/winsup/testsuite/winsup.api/pthread/priority2.c
index 0534e7ba1..f084efadf 100644
--- a/winsup/testsuite/winsup.api/pthread/priority2.c
+++ b/winsup/testsuite/winsup.api/pthread/priority2.c
@@ -54,7 +54,24 @@ void * func(void * arg)
   assert(policy == SCHED_FIFO);
   return (void *) (size_t)param.sched_priority;
 }
- 
+
+// Windows only supports 7 thread priority levels, which we map onto the 32
+// required by POSIX.  The exact mapping also depends on the overall process
+// priority class. So only a subset of values will be returned exactly by
+// pthread_getschedparam() after pthread_setschedparam().
+int doable_pri(int pri)
+{
+  switch (GetPriorityClass(GetCurrentProcess()))
+    {
+    case BELOW_NORMAL_PRIORITY_CLASS:
+      return (pri == 2) || (pri ==  8) || (pri == 10) || (pri == 12) || (pri == 14) || (pri == 16) || (pri == 30);
+    case NORMAL_PRIORITY_CLASS:
+      return (pri == 2) || (pri == 12) || (pri == 14) || (pri == 16) || (pri == 18) || (pri == 20) || (pri == 30);
+    }
+
+  return TRUE;
+}
+
 int
 main()
 {
@@ -73,7 +90,8 @@ main()
       assert(pthread_setschedparam(t, SCHED_FIFO, &param) == 0);
       assert(pthread_mutex_unlock(&startMx) == 0);
       pthread_join(t, &result);
-      assert((int)(size_t)result == param.sched_priority);
+      if (doable_pri(param.sched_priority))
+	assert((int)(size_t)result == param.sched_priority);
     }
 
   return 0;