diff --git a/src/net_processing.cpp b/src/net_processing.cpp
index 7494dd8642..81aa58a87f 100644
--- a/src/net_processing.cpp
+++ b/src/net_processing.cpp
@@ -4032,9 +4032,23 @@ void PeerManagerImpl::ProcessMessage(
             return;
         }
 
+        if (fImporting || fReindex) {
+            LogPrint(BCLog::NET, "Ignoring %s from peer=%d while importing/reindexing\n", msg_type, pfrom.GetId());
+            return;
+        }
+
         LOCK(cs_main);
-        if (m_chainman.ActiveChainstate().IsInitialBlockDownload() && !pfrom.HasPermission(NetPermissionFlags::Download)) {
-            LogPrint(BCLog::NET, "Ignoring %s from peer=%d because node is in initial block download\n", msg_type, pfrom.GetId());
+
+        // Note that if we were to be on a chain that forks from the checkpointed
+        // chain, then serving those headers to a peer that has seen the
+        // checkpointed chain would cause that peer to disconnect us. Requiring
+        // that our chainwork exceed nMinimumChainWork is a protection against
+        // being fed a bogus chain when we started up for the first time and
+        // getting partitioned off the honest network for serving that chain to
+        // others.
+        if (m_chainman.ActiveTip() == nullptr ||
+                (m_chainman.ActiveTip()->nChainWork < nMinimumChainWork && !pfrom.HasPermission(NetPermissionFlags::Download))) {
+            LogPrint(BCLog::NET, "Ignoring %s from peer=%d because active chain has too little work\n", msg_type, pfrom.GetId());
             return;
         }
 
diff --git a/test/functional/feature_minchainwork.py b/test/functional/feature_minchainwork.py
index b7932d61a3..3ac6444255 100755
--- a/test/functional/feature_minchainwork.py
+++ b/test/functional/feature_minchainwork.py
@@ -17,6 +17,7 @@ only succeeds past a given node once its nMinimumChainWork has been exceeded.
 
 import time
 
+from test_framework.p2p import P2PInterface, msg_getheaders
 from test_framework.test_framework import BitcoinTestFramework
 from test_framework.util import assert_equal
 
@@ -43,6 +44,9 @@ class MinimumChainWorkTest(BitcoinTestFramework):
         for i in range(self.num_nodes-1):
             self.connect_nodes(i+1, i)
 
+        # Set clock of node2 2 days ahead, to keep it in IBD during this test.
+        self.nodes[2].setmocktime(int(time.time()) + 48*60*60)
+
     def run_test(self):
         # Start building a chain on node0.  node2 shouldn't be able to sync until node1's
         # minchainwork is exceeded
@@ -74,6 +78,15 @@ class MinimumChainWorkTest(BitcoinTestFramework):
         assert self.nodes[1].getbestblockhash() != self.nodes[0].getbestblockhash()
         assert_equal(self.nodes[2].getblockcount(), starting_blockcount)
 
+        self.log.info("Check that getheaders requests to node2 are ignored")
+        peer = self.nodes[2].add_p2p_connection(P2PInterface())
+        msg = msg_getheaders()
+        msg.locator.vHave = [int(self.nodes[2].getbestblockhash(), 16)]
+        msg.hashstop = 0
+        peer.send_and_ping(msg)
+        time.sleep(5)
+        assert "headers" not in peer.last_message
+
         self.log.info("Generating one more block")
         self.nodes[0].generatetoaddress(1, self.nodes[0].get_deterministic_priv_key().address)
 
@@ -88,6 +101,14 @@ class MinimumChainWorkTest(BitcoinTestFramework):
         self.sync_all()
         self.log.info("Blockcounts: %s", [n.getblockcount() for n in self.nodes])
 
+        self.log.info("Test that getheaders requests to node2 are not ignored")
+        peer.send_and_ping(msg)
+        assert "headers" in peer.last_message
+
+        # Verify that node2 is in fact still in IBD (otherwise this test may
+        # not be exercising the logic we want!)
+        assert_equal(self.nodes[2].getblockchaininfo()['initialblockdownload'], True)
+
         self.log.info("Test -minimumchainwork with a non-hex value")
         self.stop_node(0)
         self.nodes[0].assert_start_raises_init_error(