diff --git a/qa/rpc-tests/p2p-acceptblock.py b/qa/rpc-tests/p2p-acceptblock.py
index fcdd1e1b9..6431f430a 100755
--- a/qa/rpc-tests/p2p-acceptblock.py
+++ b/qa/rpc-tests/p2p-acceptblock.py
@@ -40,6 +40,11 @@ The test:
    it's missing an intermediate block.
    Node1 should reorg to this longer chain.
 
+4b.Send 288 more blocks on the longer chain.
+   Node0 should process all but the last block (too far ahead in height).
+   Send all headers to Node1, and then send the last block in that chain.
+   Node1 should accept the block because it's coming from a whitelisted peer.
+
 5. Send a duplicate of the block in #3 to Node0.
    Node0 should not process the block because it is unrequested, and stay on
    the shorter chain.
@@ -126,13 +131,15 @@ class AcceptBlockTest(BitcoinTestFramework):
         # 2. Send one block that builds on each tip.
         # This should be accepted.
         blocks_h2 = []  # the height 2 blocks on each node's chain
+        block_time = time.time() + 1
         for i in xrange(2):
-            blocks_h2.append(create_block(tips[i], create_coinbase(), time.time()+1))
+            blocks_h2.append(create_block(tips[i], create_coinbase(), block_time))
             blocks_h2[i].solve()
+            block_time += 1
         test_node.send_message(msg_block(blocks_h2[0]))
         white_node.send_message(msg_block(blocks_h2[1]))
 
-        time.sleep(1)
+        time.sleep(0.5)
         assert_equal(self.nodes[0].getblockcount(), 2)
         assert_equal(self.nodes[1].getblockcount(), 2)
         print "First height 2 block accepted by both nodes"
@@ -145,7 +152,7 @@ class AcceptBlockTest(BitcoinTestFramework):
         test_node.send_message(msg_block(blocks_h2f[0]))
         white_node.send_message(msg_block(blocks_h2f[1]))
 
-        time.sleep(1)  # Give time to process the block
+        time.sleep(0.5)  # Give time to process the block
         for x in self.nodes[0].getchaintips():
             if x['hash'] == blocks_h2f[0].hash:
                 assert_equal(x['status'], "headers-only")
@@ -164,7 +171,7 @@ class AcceptBlockTest(BitcoinTestFramework):
         test_node.send_message(msg_block(blocks_h3[0]))
         white_node.send_message(msg_block(blocks_h3[1]))
 
-        time.sleep(1)
+        time.sleep(0.5)
         # Since the earlier block was not processed by node0, the new block
         # can't be fully validated.
         for x in self.nodes[0].getchaintips():
@@ -182,6 +189,45 @@ class AcceptBlockTest(BitcoinTestFramework):
         assert_equal(self.nodes[1].getblockcount(), 3)
         print "Successfully reorged to length 3 chain from whitelisted peer"
 
+        # 4b. Now mine 288 more blocks and deliver; all should be processed but
+        # the last (height-too-high) on node0.  Node1 should process the tip if
+        # we give it the headers chain leading to the tip.
+        tips = blocks_h3
+        headers_message = msg_headers()
+        all_blocks = []   # node0's blocks
+        for j in xrange(2):
+            for i in xrange(288):
+                next_block = create_block(tips[j].sha256, create_coinbase(), tips[j].nTime+1)
+                next_block.solve()
+                if j==0:
+                    test_node.send_message(msg_block(next_block))
+                    all_blocks.append(next_block)
+                else:
+                    headers_message.headers.append(CBlockHeader(next_block))
+                tips[j] = next_block
+
+        time.sleep(2)
+        for x in all_blocks:
+            try:
+                self.nodes[0].getblock(x.hash)
+                if x == all_blocks[287]:
+                    raise AssertionError("Unrequested block too far-ahead should have been ignored")
+            except:
+                if x == all_blocks[287]:
+                    print "Unrequested block too far-ahead not processed"
+                else:
+                    raise AssertionError("Unrequested block with more work should have been accepted")
+
+        headers_message.headers.pop() # Ensure the last block is unrequested
+        white_node.send_message(headers_message) # Send headers leading to tip
+        white_node.send_message(msg_block(tips[1]))  # Now deliver the tip
+        try:
+            time.sleep(0.5)
+            self.nodes[1].getblock(tips[1].hash)
+            print "Unrequested block far ahead of tip accepted from whitelisted peer"
+        except:
+            raise AssertionError("Unrequested block from whitelisted peer not accepted")
+
         # 5. Test handling of unrequested block on the node that didn't process
         # Should still not be processed (even though it has a child that has more
         # work).
@@ -204,21 +250,20 @@ class AcceptBlockTest(BitcoinTestFramework):
             test_node.last_getdata = None
             test_node.send_message(msg_inv([CInv(2, blocks_h3[0].sha256)]))
 
-        time.sleep(1)
+        time.sleep(0.5)
         with mininode_lock:
             getdata = test_node.last_getdata
 
-        # Check that the getdata is for the right block
-        assert_equal(len(getdata.inv), 1)
+        # Check that the getdata includes the right block
         assert_equal(getdata.inv[0].hash, blocks_h2f[0].sha256)
         print "Inv at tip triggered getdata for unprocessed block"
 
         # 7. Send the missing block for the third time (now it is requested)
         test_node.send_message(msg_block(blocks_h2f[0]))
 
-        time.sleep(1)
-        assert_equal(self.nodes[0].getblockcount(), 3)
-        print "Successfully reorged to length 3 chain from non-whitelisted peer"
+        time.sleep(2)
+        assert_equal(self.nodes[0].getblockcount(), 290)
+        print "Successfully reorged to longer chain from non-whitelisted peer"
 
         [ c.disconnect_node() for c in connections ]
 
diff --git a/src/main.cpp b/src/main.cpp
index 760cda5de..e0997515b 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -2841,9 +2841,15 @@ bool AcceptBlock(CBlock& block, CValidationState& state, CBlockIndex** ppindex,
 
     // Try to process all requested blocks that we don't have, but only
     // process an unrequested block if it's new and has enough work to
-    // advance our tip.
+    // advance our tip, and isn't too many blocks ahead.
     bool fAlreadyHave = pindex->nStatus & BLOCK_HAVE_DATA;
     bool fHasMoreWork = (chainActive.Tip() ? pindex->nChainWork > chainActive.Tip()->nChainWork : true);
+    // Blocks that are too out-of-order needlessly limit the effectiveness of
+    // pruning, because pruning will not delete block files that contain any
+    // blocks which are too close in height to the tip.  Apply this test
+    // regardless of whether pruning is enabled; it should generally be safe to
+    // not process unrequested blocks.
+    bool fTooFarAhead = (pindex->nHeight - chainActive.Height()) > MIN_BLOCKS_TO_KEEP;
 
     // TODO: deal better with return value and error conditions for duplicate
     // and unrequested blocks.
@@ -2851,6 +2857,7 @@ bool AcceptBlock(CBlock& block, CValidationState& state, CBlockIndex** ppindex,
     if (!fRequested) {  // If we didn't ask for it:
         if (pindex->nTx != 0) return true;  // This is a previously-processed block that was pruned
         if (!fHasMoreWork) return true;     // Don't process less-work chains
+        if (fTooFarAhead) return true;      // Block height is too high
     }
 
     if ((!CheckBlock(block, state)) || !ContextualCheckBlock(block, state, pindex->pprev)) {