diff --git a/src/pendulum/datetime.py b/src/pendulum/datetime.py
index 96aff25b..c0b167e6 100644
--- a/src/pendulum/datetime.py
+++ b/src/pendulum/datetime.py
@@ -228,8 +228,19 @@ def set(
         if tz is None:
             tz = self.tz
 
+        fold = self.fold
+        if (
+            self.tz is not None
+            and self.replace(fold=0).utcoffset() == self.replace(fold=1).utcoffset()
+        ):
+            # The current time is not ambiguous, so its fold attribute
+            # carries no meaning and must not decide how the new time
+            # is resolved if it falls in a DST gap or overlap.
+            # Use the default resolution of create() instead.
+            fold = 1
+
         return self.__class__.create(
-            year, month, day, hour, minute, second, microsecond, tz=tz, fold=self.fold
+            year, month, day, hour, minute, second, microsecond, tz=tz, fold=fold
         )
 
     @property
diff --git a/src/pendulum/tz/timezone.py b/src/pendulum/tz/timezone.py
index 28686e2d..603d852b 100644
--- a/src/pendulum/tz/timezone.py
+++ b/src/pendulum/tz/timezone.py
@@ -169,7 +169,16 @@ def convert(self, dt: _DT, raise_on_unknown_times: bool = False) -> _DT:
                 # Repeated time
                 raise AmbiguousTime(dt)
 
-            return dt.replace(tzinfo=self)
+            dt = dt.replace(tzinfo=self)
+
+            if self.utcoffset(dt.replace(fold=0)) == self.utcoffset(dt.replace(fold=1)):
+                # The local time is not ambiguous, so the fold attribute
+                # carries no meaning for it and must be set to 0 (PEP 495).
+                # Without this, times created with the default fold=1,
+                # e.g. via DateTime.create(), keep a bogus fold value.
+                dt = dt.replace(fold=0)
+
+            return dt
 
         return cast("_DT", dt.astimezone(self))
 
diff --git a/tests/datetime/test_fluent_setters.py b/tests/datetime/test_fluent_setters.py
index cedbd269..4ad46f1a 100644
--- a/tests/datetime/test_fluent_setters.py
+++ b/tests/datetime/test_fluent_setters.py
@@ -141,6 +141,15 @@ def test_fluid_at_with_transition():
     assert new.second == 0
 
 
+def test_set_keeps_fold_of_ambiguous_time():
+    d = pendulum.datetime(2023, 11, 5, 1, 30, tz="America/New_York", fold=0)
+    new = d.set(minute=45)
+
+    assert isinstance(new, datetime)
+    assert new.fold == 0
+    assert new.offset == -4 * 3600
+
+
 def test_replace_tzinfo_dst_off():
     d = pendulum.datetime(2016, 3, 27, 0, 30)  # 30 min before DST turning on
     new = d.replace(tzinfo=pendulum.timezone("Europe/Paris"))
diff --git a/tests/tz/test_timezone.py b/tests/tz/test_timezone.py
index 6ce475d3..9479f209 100644
--- a/tests/tz/test_timezone.py
+++ b/tests/tz/test_timezone.py
@@ -330,6 +330,35 @@ def test_convert_fold_attribute_is_honored():
     assert new.strftime("%z") == "-0500"
 
 
+def test_convert_unambiguous_time_has_fold_zero():
+    tz = pendulum.timezone("CET")
+    dt = datetime(2024, 5, 1)
+
+    new = tz.convert(dt)
+    assert new.fold == 0
+
+    new = tz.convert(dt.replace(fold=1))
+    assert new.fold == 0
+
+
+def test_datetime_unambiguous_time_has_fold_zero():
+    dt = pendulum.datetime(2024, 5, 1, tz="CET")
+
+    assert dt.fold == 0
+    assert dt.add(minutes=1).fold == 0
+    assert dt.add(days=1).fold == 0
+
+
+def test_datetime_ambiguous_time_keeps_fold():
+    dt = pendulum.datetime(2023, 11, 5, 1, 30, tz="America/New_York")
+
+    assert dt.fold == 1
+
+    dt = pendulum.datetime(2023, 11, 5, 1, 30, tz="America/New_York", fold=0)
+
+    assert dt.fold == 0
+
+
 def test_utcoffset_fold_attribute_is_honored():
     tz = pendulum.timezone("US/Eastern")
     dt = datetime(2014, 11, 2, 1, 30)