diff --git a/src/net_processing.cpp b/src/net_processing.cpp
index 81aa58a87f..bf883d4d86 100644
--- a/src/net_processing.cpp
+++ b/src/net_processing.cpp
@@ -5462,10 +5462,31 @@ bool PeerManagerImpl::SendMessages(CNode* pto)
         if (m_chainman.m_best_header == nullptr) {
             m_chainman.m_best_header = m_chainman.ActiveChain().Tip();
         }
-        bool fFetch = state.fPreferredDownload || (nPreferredDownload == 0 && !pto->fClient && !pto->IsAddrFetchConn()); // Download if this is a nice peer, or we have no nice peers and this one might do.
+
+        // Determine whether we might try initial headers sync or parallel
+        // block download from this peer -- this mostly affects behavior while
+        // in IBD (once out of IBD, we sync from all peers).
+        bool sync_blocks_and_headers_from_peer = false;
+        if (state.fPreferredDownload) {
+            sync_blocks_and_headers_from_peer = true;
+        } else if (!pto->fClient && !pto->IsAddrFetchConn()) {
+            // Typically this is an inbound peer. If we don't have any outbound
+            // peers, or if we aren't downloading any blocks from such peers,
+            // then allow block downloads from this peer, too.
+            // We prefer downloading blocks from outbound peers to avoid
+            // putting undue load on (say) some home user who is just making
+            // outbound connections to the network, but if our only source of
+            // the latest blocks is from an inbound peer, we have to be sure to
+            // eventually download it (and not just wait indefinitely for an
+            // outbound peer to have it).
+            if (nPreferredDownload == 0 || mapBlocksInFlight.empty()) {
+                sync_blocks_and_headers_from_peer = true;
+            }
+        }
+
         if (!state.fSyncStarted && !pto->fClient && !fImporting && !fReindex && pto->CanRelay()) {
             // Only actively request headers from a single peer, unless we're close to end of initial download.
-            if ((nSyncStarted == 0 && fFetch) || m_chainman.m_best_header->GetBlockTime() > GetAdjustedTime() - nMaxTipAge) {
+            if ((nSyncStarted == 0 && sync_blocks_and_headers_from_peer) || m_chainman.m_best_header->GetBlockTime() > GetAdjustedTime() - nMaxTipAge) {
                 state.fSyncStarted = true;
                 state.m_headers_sync_timeout = current_time + HEADERS_DOWNLOAD_TIMEOUT_BASE +
                     (
@@ -5888,7 +5909,7 @@ bool PeerManagerImpl::SendMessages(CNode* pto)
         // Message: getdata (blocks)
         //
         std::vector<CInv> vGetData;
-        if (!pto->fClient && pto->CanRelay() && ((fFetch && !pto->m_limited_node) || !m_chainman.ActiveChainstate().IsInitialBlockDownload()) && state.nBlocksInFlight < MAX_BLOCKS_IN_TRANSIT_PER_PEER) {
+        if (!pto->fClient && pto->CanRelay() && ((sync_blocks_and_headers_from_peer && !pto->m_limited_node) || !m_chainman.ActiveChainstate().IsInitialBlockDownload()) && state.nBlocksInFlight < MAX_BLOCKS_IN_TRANSIT_PER_PEER) {
             std::vector<const CBlockIndex*> vToDownload;
             NodeId staller = -1;
             FindNextBlocksToDownload(pto->GetId(), MAX_BLOCKS_IN_TRANSIT_PER_PEER - state.nBlocksInFlight, vToDownload, staller);
diff --git a/test/functional/p2p_block_sync.py b/test/functional/p2p_block_sync.py
new file mode 100755
index 0000000000..0506735971
--- /dev/null
+++ b/test/functional/p2p_block_sync.py
@@ -0,0 +1,37 @@
+#!/usr/bin/env python3
+# Copyright (c) 2022 The Bitcoin Core developers
+# Distributed under the MIT software license, see the accompanying
+# file COPYING or http://www.opensource.org/licenses/mit-license.php.
+"""Test block download
+
+Ensure that even in IBD, we'll eventually sync chain from inbound peers
+(whether we have only inbound peers or both inbound and outbound peers).
+"""
+
+from test_framework.test_framework import BitcoinTestFramework
+
+class BlockSyncTest(BitcoinTestFramework):
+
+    def set_test_params(self):
+        self.setup_clean_chain = True
+        self.num_nodes = 3
+
+    def setup_network(self):
+        self.setup_nodes()
+        # Construct a network:
+        # node0 -> node1 -> node2
+        # So node1 has both an inbound and outbound peer.
+        # In our test, we will mine a block on node0, and ensure that it makes
+        # to to both node1 and node2.
+        self.connect_nodes(0, 1)
+        self.connect_nodes(1, 2)
+
+    def run_test(self):
+        self.log.info("Setup network: node0->node1->node2")
+        self.log.info("Mining one block on node0 and verify all nodes sync")
+        self.nodes[0].generate(1)
+        self.log.info("Success!")
+
+
+if __name__ == '__main__':
+    BlockSyncTest().main()
diff --git a/test/functional/test_runner.py b/test/functional/test_runner.py
index 2a87e9c6af..3a8856d3c6 100755
--- a/test/functional/test_runner.py
+++ b/test/functional/test_runner.py
@@ -172,6 +172,7 @@ BASE_SCRIPTS = [
     'wallet_avoidreuse.py --descriptors',
     'mempool_reorg.py',
     'mempool_persist.py',
+    'p2p_block_sync.py',
     'wallet_multiwallet.py --legacy-wallet',
     'wallet_multiwallet.py --descriptors',
     'wallet_multiwallet.py --usecli',