diff --git a/Tests/test_image.py b/Tests/test_image.py
index c4e6f8ade..2d661a903 100644
--- a/Tests/test_image.py
+++ b/Tests/test_image.py
@@ -149,10 +149,11 @@ class TestImage:
             assert im.mode == "RGB"
             assert im.size == (128, 128)
 
-            temp_file = str(tmp_path / "temp.jpg")
-            if os.path.exists(temp_file):
-                os.remove(temp_file)
-            im.save(Path(temp_file))
+            for ext in (".jpg", ".jp2"):
+                temp_file = str(tmp_path / ("temp." + ext))
+                if os.path.exists(temp_file):
+                    os.remove(temp_file)
+                im.save(Path(temp_file))
 
     def test_fp_name(self, tmp_path):
         temp_file = str(tmp_path / "temp.jpg")
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index 34959cddd..5d565f613 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -2180,12 +2180,12 @@ class Image:
 
         filename = ""
         open_fp = False
-        if isPath(fp):
-            filename = fp
-            open_fp = True
-        elif isinstance(fp, Path):
+        if isinstance(fp, Path):
             filename = str(fp)
             open_fp = True
+        elif isPath(fp):
+            filename = fp
+            open_fp = True
         elif fp == sys.stdout:
             try:
                 fp = sys.stdout.buffer