diff --git a/Tests/test_file_cur.py b/Tests/test_file_cur.py
index 23055a0ad..1628007ee 100644
--- a/Tests/test_file_cur.py
+++ b/Tests/test_file_cur.py
@@ -26,6 +26,7 @@ class TestFileCur(PillowTestCase):
         no_cursors_file = "Tests/images/no_cursors.cur"
 
         cur = CurImagePlugin.CurImageFile(TEST_FILE)
+        cur.fp.close()
         with open(no_cursors_file, "rb") as cur.fp:
             self.assertRaises(TypeError, cur._open)
 
diff --git a/Tests/test_file_icns.py b/Tests/test_file_icns.py
index b19cf2e4c..5e0f377c4 100644
--- a/Tests/test_file_icns.py
+++ b/Tests/test_file_icns.py
@@ -17,7 +17,10 @@ class TestFileIcns(PillowTestCase):
         # Loading this icon by default should result in the largest size
         # (512x512@2x) being loaded
         im = Image.open(TEST_FILE)
-        im.load()
+
+        # Assert that there is no unclosed file warning
+        self.assert_warning(None, im.load)
+
         self.assertEqual(im.mode, "RGBA")
         self.assertEqual(im.size, (1024, 1024))
         self.assertEqual(im.format, "ICNS")
diff --git a/Tests/test_file_png.py b/Tests/test_file_png.py
index c958c0b39..ca7d3c039 100644
--- a/Tests/test_file_png.py
+++ b/Tests/test_file_png.py
@@ -327,7 +327,9 @@ class TestFilePng(PillowTestCase):
         # Check open/load/verify exception (@PIL150)
 
         im = Image.open(TEST_PNG_FILE)
-        im.verify()
+
+        # Assert that there is no unclosed file warning
+        self.assert_warning(None, im.verify)
 
         im = Image.open(TEST_PNG_FILE)
         im.load()
diff --git a/src/PIL/IcnsImagePlugin.py b/src/PIL/IcnsImagePlugin.py
index d156b240f..2ea66675f 100644
--- a/src/PIL/IcnsImagePlugin.py
+++ b/src/PIL/IcnsImagePlugin.py
@@ -311,6 +311,8 @@ class IcnsImageFile(ImageFile.ImageFile):
         self.im = im.im
         self.mode = im.mode
         self.size = im.size
+        if self._exclusive_fp:
+            self.fp.close()
         self.fp = None
         self.icns = None
         self.tile = ()
diff --git a/src/PIL/PngImagePlugin.py b/src/PIL/PngImagePlugin.py
index 15077fceb..b89bd0efc 100644
--- a/src/PIL/PngImagePlugin.py
+++ b/src/PIL/PngImagePlugin.py
@@ -600,6 +600,8 @@ class PngImageFile(ImageFile.ImageFile):
         self.png.verify()
         self.png.close()
 
+        if self._exclusive_fp:
+            self.fp.close()
         self.fp = None
 
     def load_prepare(self):