diff --git a/PIL/Jpeg2KImagePlugin.py b/PIL/Jpeg2KImagePlugin.py
index 66069802e..0a7a6e297 100644
--- a/PIL/Jpeg2KImagePlugin.py
+++ b/PIL/Jpeg2KImagePlugin.py
@@ -172,18 +172,16 @@ class Jpeg2KImageFile(ImageFile.ImageFile):
         fd = -1
         length = -1
 
-        if hasattr(self.fp, "fileno"):
+        try:
+            fd = self.fp.fileno()
+            length = os.fstat(fd).st_size
+        except:
+            fd = -1
             try:
-                fd = self.fp.fileno()
-                length = os.fstat(fd).st_size
-            except:
-                fd = -1
-        elif hasattr(self.fp, "seek"):
-            try:
-                pos = f.tell()
-                f.seek(0, 2)
-                length = f.tell()
-                f.seek(pos, 0)
+                pos = self.fp.tell()
+                self.fp.seek(0, 2)
+                length = self.fp.tell()
+                self.fp.seek(pos, 0)
             except:
                 length = -1
 
diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index b763687f7..e115df3a8 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -39,6 +39,14 @@ class TestFileJpeg2k(PillowTestCase):
         self.assertEqual(im.size, (640, 480))
         self.assertEqual(im.format, 'JPEG2000')
 
+    def test_bytesio(self):
+        with open('Tests/images/test-card-lossless.jp2', 'rb') as f:
+            data = BytesIO(f.read())
+        im = Image.open(data)
+        im.load()
+        print ("bytesio")
+        self.assert_image_similar(im, test_card, 1.0e-3)
+
     # These two test pre-written JPEG 2000 files that were not written with
     # PIL (they were made using Adobe Photoshop)