diff --git a/paramiko/sftp_file.py b/paramiko/sftp_file.py
index 02c6e76..7d9b8f4 100644
--- a/paramiko/sftp_file.py
+++ b/paramiko/sftp_file.py
@@ -44,6 +44,7 @@ class SFTPFile (BufferedFile):
         BufferedFile._set_mode(self, mode, bufsize)
         self.pipelined = False
         self._prefetching = False
+        self._prefetch_done = False
         self._prefetch_so_far = 0
         self._prefetch_size = 0
         self._prefetch_data = {}
@@ -83,29 +84,48 @@ class SFTPFile (BufferedFile):
             pass
 
     def _read_prefetch(self, size):
+        """
+        read data out of the prefetch buffer, if possible.  if the data isn't
+        in the buffer, return None.  otherwise, behaves like a normal read.
+        """
         # while not closed, and haven't fetched past the current position, and haven't reached EOF...
         while (self._prefetch_so_far <= self._realpos) and \
             (self._prefetch_so_far < self._prefetch_size) and not self._closed:
+            if self._prefetch_done:
+                return None
             self.sftp._read_response()
         self._check_exception()
         k = self._prefetch_data.keys()
-        k.sort()
-        while (len(k) > 0) and (k[0] + len(self._prefetch_data[k[0]]) <= self._realpos):
-            # done with that block
-            del self._prefetch_data[k[0]]
-            k.pop(0)
         if len(k) == 0:
             self._prefetching = False
             return ''
-        assert k[0] <= self._realpos
-        buf_offset = self._realpos - k[0]
-        buf_length = len(self._prefetch_data[k[0]]) - buf_offset
-        return self._prefetch_data[k[0]][buf_offset : buf_offset + buf_length]
+
+        # find largest offset < realpos
+        pos_list = [i for i in k if i <= self._realpos]
+        if len(pos_list) == 0:
+            return None
+        index = max(pos_list)
+        prefetch = self._prefetch_data[index]
+        del self._prefetch_data[index]
+        
+        buf_offset = self._realpos - index
+        if buf_offset > 0:
+            self._prefetch_data[index] = prefetch[:buf_offset]
+            prefetch = prefetch[buf_offset:]
+        if buf_offset >= len(prefetch):
+            # it's not here.
+            return None
+        if size < len(prefetch):
+            self._prefetch_data[self._realpos + size] = prefetch[size:]
+            prefetch = prefetch[:size]
+        return prefetch
         
     def _read(self, size):
         size = min(size, self.MAX_REQUEST_SIZE)
         if self._prefetching:
-            return self._read_prefetch(size)
+            data = self._read_prefetch(size)
+            if data is not None:
+                return data
         t, msg = self.sftp._request(CMD_READ, self.handle, long(self._realpos), int(size))
         if t != CMD_DATA:
             raise SFTPError('Expected data')
@@ -333,6 +353,7 @@ class SFTPFile (BufferedFile):
         size = self.stat().st_size
         # queue up async reads for the rest of the file
         self._prefetching = True
+        self._prefetch_done = False
         self._prefetch_so_far = self._realpos
         self._prefetch_size = size
         self._prefetch_data = {}
@@ -371,6 +392,8 @@ class SFTPFile (BufferedFile):
         data = msg.get_string()
         self._prefetch_data[self._prefetch_so_far] = data
         self._prefetch_so_far += len(data)
+        if self._prefetch_so_far == self._prefetch_size:
+            self._prefetch_done = True
     
     def _check_exception(self):
         "if there's a saved exception, raise & clear it"