diff --git a/Lib/datetime.py b/Lib/datetime.py
index d4c7a1f..0adf1dd 100644
--- a/Lib/datetime.py
+++ b/Lib/datetime.py
@@ -2269,7 +2269,7 @@
         raise TypeError("fromutc() argument must be a datetime instance"
                         " or None")
 
-    _maxoffset = timedelta(hours=23, minutes=59)
+    _maxoffset = timedelta(hours=24, microseconds=-1)
     _minoffset = -_maxoffset
 
     @staticmethod
@@ -2293,8 +2293,11 @@
         return f'UTC{sign}{hours:02d}:{minutes:02d}'
 
 timezone.utc = timezone._create(timedelta(0))
-timezone.min = timezone._create(timezone._minoffset)
-timezone.max = timezone._create(timezone._maxoffset)
+# bpo-37642: These attributes are rounded to the nearest minute for backwards
+# compatibility, even though the constructor will accept a wider range of
+# values. This may change in the future.
+timezone.min = timezone._create(-timedelta(hours=23, minutes=59))
+timezone.max = timezone._create(timedelta(hours=23, minutes=59))
 _EPOCH = datetime(1970, 1, 1, tzinfo=timezone.utc)
 
 # Some time zone algebra.  For a datetime x, let