diff --git a/psutil/tests/test_process.py b/psutil/tests/test_process.py
index 2a2af93c6..181097e3b 100755
--- a/psutil/tests/test_process.py
+++ b/psutil/tests/test_process.py
@@ -799,19 +799,29 @@ def test_nice(self):
         init = p.nice()
         try:
             if WINDOWS:
-                for prio in [psutil.NORMAL_PRIORITY_CLASS,
-                             psutil.IDLE_PRIORITY_CLASS,
+                # A CI runner may limit our maximum priority, which will break
+                # this test. Instead, we test in order of increasing priority,
+                # and match either the expected value or the highest so far.
+                highest_prio = None
+                for prio in [psutil.IDLE_PRIORITY_CLASS,
                              psutil.BELOW_NORMAL_PRIORITY_CLASS,
-                             psutil.REALTIME_PRIORITY_CLASS,
+                             psutil.NORMAL_PRIORITY_CLASS,
+                             psutil.ABOVE_NORMAL_PRIORITY_CLASS,
                              psutil.HIGH_PRIORITY_CLASS,
-                             psutil.ABOVE_NORMAL_PRIORITY_CLASS]:
+                             psutil.REALTIME_PRIORITY_CLASS]:
                     with self.subTest(prio=prio):
                         try:
                             p.nice(prio)
                         except psutil.AccessDenied:
                             pass
                         else:
-                            self.assertEqual(p.nice(), prio)
+                            new_prio = p.nice()
+                            if CI_TESTING:
+                                if new_prio == prio or highest_prio is None:
+                                    highest_prio = prio
+                                self.assertEqual(new_prio, highest_prio)
+                            else:
+                                self.assertEqual(new_prio, prio)
             else:
                 try:
                     if hasattr(os, "getpriority"):
@@ -846,7 +856,13 @@ def test_username(self):
         username = p.username()
         if WINDOWS:
             domain, username = username.split('\\')
-            self.assertEqual(username, getpass.getuser())
+            getpass_user = getpass.getuser()
+            if getpass_user.endswith('$'):
+                # When running as a service account (most likely to be
+                # NetworkService), these user name calculations don't produce
+                # the same result, causing the test to fail.
+                raise unittest.SkipTest('running as service account')
+            self.assertEqual(username, getpass_user)
             if 'USERDOMAIN' in os.environ:
                 self.assertEqual(domain, os.environ['USERDOMAIN'])
         else:
diff --git a/psutil/tests/test_windows.py b/psutil/tests/test_windows.py
index 55b6bc7b1..7a843bc38 100755
--- a/psutil/tests/test_windows.py
+++ b/psutil/tests/test_windows.py
@@ -86,13 +86,14 @@ def test_cpu_count_vs_GetSystemInfo(self):
 
     def test_cpu_count_logical_vs_wmi(self):
         w = wmi.WMI()
-        proc = w.Win32_Processor()[0]
-        self.assertEqual(psutil.cpu_count(), proc.NumberOfLogicalProcessors)
+        procs = sum(proc.NumberOfLogicalProcessors
+                    for proc in w.Win32_Processor())
+        self.assertEqual(psutil.cpu_count(), procs)
 
     def test_cpu_count_cores_vs_wmi(self):
         w = wmi.WMI()
-        proc = w.Win32_Processor()[0]
-        self.assertEqual(psutil.cpu_count(logical=False), proc.NumberOfCores)
+        cores = sum(proc.NumberOfCores for proc in w.Win32_Processor())
+        self.assertEqual(psutil.cpu_count(logical=False), cores)
 
     def test_cpu_count_vs_cpu_times(self):
         self.assertEqual(psutil.cpu_count(),
@@ -213,7 +214,7 @@ def test_boot_time(self):
             wmi_btime_str, "%Y%m%d%H%M%S")
         psutil_dt = datetime.datetime.fromtimestamp(psutil.boot_time())
         diff = abs((wmi_btime_dt - psutil_dt).total_seconds())
-        self.assertLessEqual(diff, 3)
+        self.assertLessEqual(diff, 5)
 
     def test_boot_time_fluctuation(self):
         # https://github.com/giampaolo/psutil/issues/1007
@@ -351,12 +352,23 @@ def test_ctrl_signals(self):
                           p.send_signal, signal.CTRL_BREAK_EVENT)
 
     def test_username(self):
-        self.assertEqual(psutil.Process().username(),
-                         win32api.GetUserNameEx(win32con.NameSamCompatible))
+        name = win32api.GetUserNameEx(win32con.NameSamCompatible)
+        if name.endswith('$'):
+            # When running as a service account (most likely to be
+            # NetworkService), these user name calculations don't produce the
+            # same result, causing the test to fail.
+            raise unittest.SkipTest('running as service account')
+        self.assertEqual(psutil.Process().username(), name)
 
     def test_cmdline(self):
-        sys_value = re.sub(' +', ' ', win32api.GetCommandLine()).strip()
+        sys_value = re.sub('[ ]+', ' ', win32api.GetCommandLine()).strip()
         psutil_value = ' '.join(psutil.Process().cmdline())
+        if sys_value[0] == '"' != psutil_value[0]:
+            # The PyWin32 command line may retain quotes around argv[0] if they
+            # were used unnecessarily, while psutil will omit them. So remove
+            # the first 2 quotes from sys_value if not in psutil_value.
+            # A path to an executable will not contain quotes, so this is safe.
+            sys_value = sys_value.replace('"', '', 2)
         self.assertEqual(sys_value, psutil_value)
 
     # XXX - occasional failures