diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index 1a1337729e0c4c..d7c404e9ff6c0c 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -232,19 +232,19 @@ def __init__(self, filename, when='h', interval=1, backupCount=0,
         if self.when == 'S':
             self.interval = 1 # one second
             self.suffix = "%Y-%m-%d_%H-%M-%S"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}-\d{2}(\.\w+)?$"
+            extMatch = r"(?<!\d)\d{4}-\d{2}-\d{2}_\d{2}-\d{2}-\d{2}(?!\d)"
         elif self.when == 'M':
             self.interval = 60 # one minute
             self.suffix = "%Y-%m-%d_%H-%M"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}(\.\w+)?$"
+            extMatch = r"(?<!\d)\d{4}-\d{2}-\d{2}_\d{2}-\d{2}(?!\d)"
         elif self.when == 'H':
             self.interval = 60 * 60 # one hour
             self.suffix = "%Y-%m-%d_%H"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}(\.\w+)?$"
+            extMatch = r"(?<!\d)\d{4}-\d{2}-\d{2}_\d{2}(?!\d)"
         elif self.when == 'D' or self.when == 'MIDNIGHT':
             self.interval = 60 * 60 * 24 # one day
             self.suffix = "%Y-%m-%d"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}(\.\w+)?$"
+            extMatch = r"(?<!\d)\d{4}-\d{2}-\d{2}(?!\d)"
         elif self.when.startswith('W'):
             self.interval = 60 * 60 * 24 * 7 # one week
             if len(self.when) != 2:
@@ -253,11 +253,17 @@ def __init__(self, filename, when='h', interval=1, backupCount=0,
                 raise ValueError("Invalid day specified for weekly rollover: %s" % self.when)
             self.dayOfWeek = int(self.when[1])
             self.suffix = "%Y-%m-%d"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}(\.\w+)?$"
+            extMatch = r"(?<!\d)\d{4}-\d{2}-\d{2}(?!\d)"
         else:
             raise ValueError("Invalid rollover interval specified: %s" % self.when)
 
-        self.extMatch = re.compile(self.extMatch, re.ASCII)
+        # extMatch is a pattern for matching a datetime suffix in a file name.
+        # After custom naming, it is no longer guaranteed to be separated by
+        # periods from other parts of the filename.  The lookup statements
+        # (?<!\d) and (?!\d) ensure that the datetime suffix (which itself
+        # starts and ends with digits) is not preceded or followed by digits.
+        # This reduces the number of false matches and improves performance.
+        self.extMatch = re.compile(extMatch, re.ASCII)
         self.interval = self.interval * interval # multiply by units requested
         # The following line added because the filename passed in could be a
         # path object (see Issue #27493), but self.baseFilename will be a string
@@ -376,31 +382,22 @@ def getFilesToDelete(self):
             for fileName in fileNames:
                 if fileName[:plen] == prefix:
                     suffix = fileName[plen:]
-                    if self.extMatch.match(suffix):
+                    if self.extMatch.fullmatch(suffix):
                         result.append(os.path.join(dirName, fileName))
         else:
-            # See bpo-44753: Don't use the extension when computing the prefix.
-            n, e = os.path.splitext(baseName)
-            prefix = n + '.'
-            plen = len(prefix)
             for fileName in fileNames:
-                # Our files could be just about anything after custom naming, but
-                # likely candidates are of the form
-                # foo.log.DATETIME_SUFFIX or foo.DATETIME_SUFFIX.log
-                if (not fileName.startswith(baseName) and fileName.endswith(e) and
-                    len(fileName) > (plen + 1) and not fileName[plen+1].isdigit()):
-                    continue
+                # Our files could be just about anything after custom naming,
+                # but they should contain the datetime suffix.
+                # Try to find the datetime suffix in the file name and verify
+                # that the file name can be generated by this handler.
+                m = self.extMatch.search(fileName)
+                while m:
+                    dfn = self.namer(self.baseFilename + "." + m[0])
+                    if os.path.basename(dfn) == fileName:
+                        result.append(os.path.join(dirName, fileName))
+                        break
+                    m = self.extMatch.search(fileName, m.start() + 1)
 
-                if fileName[:plen] == prefix:
-                    suffix = fileName[plen:]
-                    # See bpo-45628: The date/time suffix could be anywhere in the
-                    # filename
-
-                    parts = suffix.split('.')
-                    for part in parts:
-                        if self.extMatch.match(part):
-                            result.append(os.path.join(dirName, fileName))
-                            break
         if len(result) < self.backupCount:
             result = []
         else:
diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index e3e9f08a089aae..574f9517da4128 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -5834,7 +5834,7 @@ def test_compute_files_to_delete(self):
         for i in range(10):
             times.append(dt.strftime('%Y-%m-%d_%H-%M-%S'))
             dt += datetime.timedelta(seconds=5)
-        prefixes = ('a.b', 'a.b.c', 'd.e', 'd.e.f')
+        prefixes = ('a.b', 'a.b.c', 'd.e', 'd.e.f', 'g')
         files = []
         rotators = []
         for prefix in prefixes:
@@ -5847,10 +5847,22 @@ def test_compute_files_to_delete(self):
             if prefix.startswith('a.b'):
                 for t in times:
                     files.append('%s.log.%s' % (prefix, t))
-            else:
-                rotator.namer = lambda name: name.replace('.log', '') + '.log'
+            elif prefix.startswith('d.e'):
+                def namer(filename):
+                    dirname, basename = os.path.split(filename)
+                    basename = basename.replace('.log', '') + '.log'
+                    return os.path.join(dirname, basename)
+                rotator.namer = namer
                 for t in times:
                     files.append('%s.%s.log' % (prefix, t))
+            elif prefix == 'g':
+                def namer(filename):
+                    dirname, basename = os.path.split(filename)
+                    basename = 'g' + basename[6:] + '.oldlog'
+                    return os.path.join(dirname, basename)
+                rotator.namer = namer
+                for t in times:
+                    files.append('g%s.oldlog' % t)
         # Create empty files
         for fn in files:
             p = os.path.join(wd, fn)
@@ -5860,18 +5872,23 @@ def test_compute_files_to_delete(self):
         for i, prefix in enumerate(prefixes):
             rotator = rotators[i]
             candidates = rotator.getFilesToDelete()
-            self.assertEqual(len(candidates), 3)
+            self.assertEqual(len(candidates), 3, candidates)
             if prefix.startswith('a.b'):
                 p = '%s.log.' % prefix
                 for c in candidates:
                     d, fn = os.path.split(c)
                     self.assertTrue(fn.startswith(p))
-            else:
+            elif prefix.startswith('d.e'):
                 for c in candidates:
                     d, fn = os.path.split(c)
-                    self.assertTrue(fn.endswith('.log'))
+                    self.assertTrue(fn.endswith('.log'), fn)
                     self.assertTrue(fn.startswith(prefix + '.') and
                                     fn[len(prefix) + 2].isdigit())
+            elif prefix == 'g':
+                for c in candidates:
+                    d, fn = os.path.split(c)
+                    self.assertTrue(fn.endswith('.oldlog'))
+                    self.assertTrue(fn.startswith('g') and fn[1].isdigit())
 
     def test_compute_files_to_delete_same_filename_different_extensions(self):
         # See GH-93205 for background
@@ -5895,6 +5912,8 @@ def test_compute_files_to_delete_same_filename_different_extensions(self):
             rotators.append(rotator)
             for t in times:
                 files.append('%s.%s' % (prefix, t))
+        for t in times:
+            files.append('a.log.%s.c' % t)
         # Create empty files
         for f in files:
             (wd / f).touch()
@@ -5903,11 +5922,11 @@ def test_compute_files_to_delete_same_filename_different_extensions(self):
             backupCount = i+1
             rotator = rotators[i]
             candidates = rotator.getFilesToDelete()
-            self.assertEqual(len(candidates), n_files - backupCount)
-            matcher = re.compile(r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}-\d{2}(\.\w+)?$")
+            self.assertEqual(len(candidates), n_files - backupCount, candidates)
+            matcher = re.compile(r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}-\d{2}\Z")
             for c in candidates:
                 d, fn = os.path.split(c)
-                self.assertTrue(fn.startswith(prefix))
+                self.assertTrue(fn.startswith(prefix+'.'))
                 suffix = fn[(len(prefix)+1):]
                 self.assertRegex(suffix, matcher)
 
diff --git a/Misc/NEWS.d/next/Library/2024-02-22-11-29-27.gh-issue-115809.9H1DhB.rst b/Misc/NEWS.d/next/Library/2024-02-22-11-29-27.gh-issue-115809.9H1DhB.rst
new file mode 100644
index 00000000000000..2a47efbae5c84d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-02-22-11-29-27.gh-issue-115809.9H1DhB.rst
@@ -0,0 +1,4 @@
+Improve algorithm for computing which rolled-over log files to delete in
+:class:`logging.TimedRotatingFileHandler`. It is now reliable for handlers
+without ``namer`` and with arbitrary deterministic ``namer`` that leaves the
+datetime part in the file name unmodified.