diff --git a/HISTORY.rst b/HISTORY.rst
index 5221a123d..981355127 100644
--- a/HISTORY.rst
+++ b/HISTORY.rst
@@ -8,7 +8,7 @@
 - 2366_, [Windows]: log debug message when using slower process APIs.
 - 2375_, [macOS]: provide arm64 wheels.  (patch by Matthieu Darbois)
 - 2396_: `process_iter()`_ no longer pre-emptively checks whether PIDs have
-  been reused. As such it's around 20x times faster.
+  been reused. This makes `process_iter()`_ around 20x times faster.
 - 2396_: a new ``psutil.process_iter.cache_clear()`` API can be used the clear
   `process_iter()`_ internal cache.
 
diff --git a/psutil/__init__.py b/psutil/__init__.py
index 2d88a0289..934013819 100644
--- a/psutil/__init__.py
+++ b/psutil/__init__.py
@@ -608,16 +608,15 @@ def is_running(self):
             return False
         try:
             # Checking if PID is alive is not enough as the PID might
-            # have been reused by another process: we also want to
-            # verify process identity.
-            # Process identity / uniqueness over time is guaranteed by
-            # (PID + creation time) and that is verified in __eq__.
+            # have been reused by another process. Process identity /
+            # uniqueness over time is guaranteed by (PID + creation
+            # time) and that is verified in __eq__.
             self._pid_reused = self != Process(self.pid)
             if self._pid_reused:
-                self._gone = True
                 # remove this PID from `process_iter()` internal cache
                 _pmap.pop(self.pid, None)
-            return not self._pid_reused
+                raise NoSuchProcess(self.pid)
+            return True
         except ZombieProcess:
             # We should never get here as it's already handled in
             # Process.__init__; here just for extra safety.