diff --git a/PIL/TiffImagePlugin.py b/PIL/TiffImagePlugin.py
index 4b93295b7..ef271bcf3 100644
--- a/PIL/TiffImagePlugin.py
+++ b/PIL/TiffImagePlugin.py
@@ -970,6 +970,7 @@ class TiffImageFile(ImageFile.ImageFile):
             self.__frame += 1
         self.fp.seek(self._frame_pos[frame])
         self.tag_v2.load(self.fp)
+        self.__next = self.tag_v2.next
         # fill the legacy tag/ifd entries
         self.tag = self.ifd = ImageFileDirectory_v1.from_v2(self.tag_v2)
         self.__frame = frame
@@ -1009,6 +1010,12 @@ class TiffImageFile(ImageFile.ImageFile):
             return self._load_libtiff()
         return super(TiffImageFile, self).load()
 
+    def load_end(self):
+        # allow closing if we're on the first frame, there's no next
+        # This is the ImageFile.load path only, libtiff specific below.
+        if self.__frame == 0 and not self.__next:
+            self._exclusive_fp = True
+
     def _load_libtiff(self):
         """ Overload method triggered when we detect a compressed tiff
             Calls out to libtiff """
@@ -1087,15 +1094,13 @@ class TiffImageFile(ImageFile.ImageFile):
         self.readonly = 0
         # libtiff closed the fp in a, we need to close self.fp, if possible
         if hasattr(self.fp, 'close'):
-            if not self.__next:
+            if self.__frame == 0 and not self.__next:
                 self.fp.close()
         self.fp = None  # might be shared
 
         if err < 0:
             raise IOError(err)
 
-        self.load_end()
-
         return Image.Image.load(self)
 
     def _setup(self):