diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index 3d2d57b..c376ee4 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -158,7 +158,13 @@
     """
     Read the ZIP64 end-of-archive records and use that to update endrec
     """
-    fpin.seek(offset - sizeEndCentDir64Locator, 2)
+    try:
+        fpin.seek(offset - sizeEndCentDir64Locator, 2)
+    except IOError:
+        # If the seek fails, the file is not large enough to contain a ZIP64
+        # end-of-archive record, so just return the end record we were given.
+        return endrec
+
     data = fpin.read(sizeEndCentDir64Locator)
     sig, diskno, reloff, disks = struct.unpack(structEndArchive64Locator, data)
     if sig != stringEndArchive64Locator:
@@ -723,14 +729,22 @@
         if key == 'r':
             self._GetContents()
         elif key == 'w':
-            pass
+            # set the modified flag so central directory gets written
+            # even if no files are added to the archive
+            self._didModify = True
         elif key == 'a':
-            try:                        # See if file is a zip file
+            try:
+                # See if file is a zip file
                 self._RealGetContents()
                 # seek to start of directory and overwrite
                 self.fp.seek(self.start_dir, 0)
-            except BadZipfile:          # file is not a zip file, just append
+            except BadZipfile:
+                # file is not a zip file, just append
                 self.fp.seek(0, 2)
+
+                # set the modified flag so central directory gets written
+                # even if no files are added to the archive
+                self._didModify = True
         else:
             if not self._filePassed:
                 self.fp.close()
@@ -751,7 +765,10 @@
     def _RealGetContents(self):
         """Read in the table of contents for the ZIP file."""
         fp = self.fp
-        endrec = _EndRecData(fp)
+        try:
+            endrec = _EndRecData(fp)
+        except IOError:
+            raise BadZipfile("File is not a zip file")
         if not endrec:
             raise BadZipfile("File is not a zip file")
         if self.debug > 1: