diff --git a/numpy/_core/_methods.py b/numpy/_core/_methods.py
index 374fad91d90c..9d5914968388 100644
--- a/numpy/_core/_methods.py
+++ b/numpy/_core/_methods.py
@@ -93,12 +93,39 @@ def _clip(a, min=None, max=None, out=None, **kwargs):
     if min is None and max is None:
         raise ValueError("One of max or min must be given")
 
-    if min is None:
-        return um.minimum(a, max, out=out, **kwargs)
-    elif max is None:
-        return um.maximum(a, min, out=out, **kwargs)
-    else:
-        return um.clip(a, min, max, out=out, **kwargs)
+    try:
+        if min is None:
+            return um.minimum(a, max, out=out, **kwargs)
+        elif max is None:
+            return um.maximum(a, min, out=out, **kwargs)
+        else:
+            return um.clip(a, min, max, out=out, **kwargs)
+    except OverflowError:
+        # If there were python ints, an OverflowError due NEP-50 casting
+        # might be responsible. In that case, we try again.
+        # (We do not do this up front since this is a rare case, and
+        # we do not want to slow down the common path.)
+        if a.dtype.kind not in "iu":
+            raise
+
+        # Circular import if done on top.
+        from numpy._core.getlimits import iinfo
+        a_info = iinfo(a.dtype)
+        changed = False
+        if isinstance(min, int) and min < a_info.min:
+            min = a_info.min
+            changed = True
+        if isinstance(max, int) and max > a_info.max:
+            max = a_info.max
+            changed = True
+        if not changed:
+            raise
+        # try/except just in case the error was unrelated somehow.
+        try:
+            return _clip(a, min, max, out=out, **kwargs)
+        except Exception:
+            pass
+        raise
 
 def _mean(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
     arr = asanyarray(a)
diff --git a/numpy/_core/tests/test_multiarray.py b/numpy/_core/tests/test_multiarray.py
index 918d6b24eac3..9f2ac8234ff8 100644
--- a/numpy/_core/tests/test_multiarray.py
+++ b/numpy/_core/tests/test_multiarray.py
@@ -5015,17 +5015,28 @@ def test_basic(self):
             self._clip_type(
                 'uint', 1024, 10, 100, inplace=inplace)
 
-    @pytest.mark.parametrize("inplace", [False, True])
-    def test_int_range_error(self, inplace):
-        # E.g. clipping uint with negative integers fails to promote
-        # (changed with NEP 50 and may be adaptable)
-        # Similar to last check in `test_basic`
-        x = (np.random.random(1000) * 255).astype("uint8")
-        with pytest.raises(OverflowError):
-            x.clip(-1, 10, out=x if inplace else None)
-
-        with pytest.raises(OverflowError):
-            x.clip(0, 256, out=x if inplace else None)
+    @pytest.mark.parametrize("do_inplace, min, max, emin, emax", [
+        (True, -1, 10, 0, 10),
+        (True, -1, None, 0, 255),
+        (False, np.int8(-1), None, 0, 255),
+        (True, 10, 400, 10, 255),
+        (True, None, 400, 0, 255),
+        (True, -10, 256, 0, 255),
+        (False, np.int8(-10), 256, 0, 255),
+        (False, -10, np.uint16(256), 0, 255),
+    ])
+    def test_int_out_of_range(self, do_inplace, min, max, emin, emax):
+        # E.g. clipping uint with negative python integers fails to promote
+        # for ufunc, but we special-case it in _methods._clip.
+        # For numpy integers, promotion works, but then the output dtype
+        # changes, so we cannot do this in-place.
+        x = np.arange(0, 256, dtype="uint8")
+        result = x.clip(min, max)
+        self._check_range(result, emin, emax)
+        if do_inplace:
+            result2 = x.clip(min, max, out=x)
+            assert result2 is x
+            assert_array_equal(result2, result)
 
     def test_record_array(self):
         rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],