diff --git a/Tests/test_image.py b/Tests/test_image.py
index 615e00e40da..80f6583d8d9 100644
--- a/Tests/test_image.py
+++ b/Tests/test_image.py
@@ -1016,6 +1016,11 @@ def test_fli_overrun2(self):
             except OSError as e:
                 assert str(e) == "buffer overrun when reading image file"
 
+    def test_exit_fp(self):
+        with Image.new("L", (1, 1)) as im:
+            pass
+        assert not hasattr(im, "fp")
+
     def test_close_graceful(self, caplog):
         with Image.open("Tests/images/hopper.jpg") as im:
             copy = im.copy()
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index 045a06080e9..613d9462a60 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -530,15 +530,19 @@ def _new(self, im):
     def __enter__(self):
         return self
 
+    def _close_fp(self):
+        if getattr(self, "_fp", False):
+            if self._fp != self.fp:
+                self._fp.close()
+            self._fp = DeferredError(ValueError("Operation on closed image"))
+        if self.fp:
+            self.fp.close()
+
     def __exit__(self, *args):
-        if hasattr(self, "fp") and getattr(self, "_exclusive_fp", False):
-            if getattr(self, "_fp", False):
-                if self._fp != self.fp:
-                    self._fp.close()
-                self._fp = DeferredError(ValueError("Operation on closed image"))
-            if self.fp:
-                self.fp.close()
-        self.fp = None
+        if hasattr(self, "fp"):
+            if getattr(self, "_exclusive_fp", False):
+                self._close_fp()
+            self.fp = None
 
     def close(self):
         """
@@ -554,12 +558,7 @@ def close(self):
         """
         if hasattr(self, "fp"):
             try:
-                if getattr(self, "_fp", False):
-                    if self._fp != self.fp:
-                        self._fp.close()
-                    self._fp = DeferredError(ValueError("Operation on closed image"))
-                if self.fp:
-                    self.fp.close()
+                self._close_fp()
                 self.fp = None
             except Exception as msg:
                 logger.debug("Error closing: %s", msg)