diff --git a/test/functional/p2p_headers_sync_with_minchainwork.py b/test/functional/p2p_headers_sync_with_minchainwork.py
new file mode 100755
index 00000000000..8008125ed65
--- /dev/null
+++ b/test/functional/p2p_headers_sync_with_minchainwork.py
@@ -0,0 +1,66 @@
+#!/usr/bin/env python3
+# Copyright (c) 2019-2021 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 that we reject low difficulty headers to prevent our block tree from filling up with useless bloat"""
+
+from test_framework.test_framework import BitcoinTestFramework
+
+NODE1_BLOCKS_REQUIRED = 15
+NODE2_BLOCKS_REQUIRED = 2047
+
+
+class RejectLowDifficultyHeadersTest(BitcoinTestFramework):
+    def set_test_params(self):
+        self.setup_clean_chain = True
+        self.num_nodes = 3
+        # Node0 has no required chainwork; node1 requires 15 blocks on top of the genesis block; node2 requires 2047
+        self.extra_args = [["-minimumchainwork=0x0"], ["-minimumchainwork=0x1f"], ["-minimumchainwork=0x1000"]]
+
+    def setup_network(self):
+        self.setup_nodes()
+        self.connect_nodes(0, 1)
+        self.connect_nodes(0, 2)
+        self.sync_all()
+
+    def test_chains_sync_when_long_enough(self):
+        self.log.info("Generate blocks on the node with no required chainwork, and verify nodes 1 and 2 have no new headers in their headers tree")
+        with self.nodes[1].assert_debug_log(expected_msgs=["[net] Ignoring low-work chain (height=14)"]), self.nodes[2].assert_debug_log(expected_msgs=["[net] Ignoring low-work chain (height=14)"]):
+            self.generate(self.nodes[0], NODE1_BLOCKS_REQUIRED-1, sync_fun=self.no_op)
+
+        for node in self.nodes[1:]:
+            chaintips = node.getchaintips()
+            assert(len(chaintips) == 1)
+            assert {
+                'height': 0,
+                'hash': '0f9188f13cb7b2c71f2a335e3a4fc328bf5beb436012afca590b1a11466e2206',
+                'branchlen': 0,
+                'status': 'active',
+            } in chaintips
+
+        self.log.info("Generate more blocks to satisfy node1's minchainwork requirement, and verify node2 still has no new headers in headers tree")
+        with self.nodes[2].assert_debug_log(expected_msgs=["[net] Ignoring low-work chain (height=15)"]):
+            self.generate(self.nodes[0], NODE1_BLOCKS_REQUIRED - self.nodes[0].getblockcount(), sync_fun=self.no_op)
+        self.sync_blocks(self.nodes[0:2])
+
+        assert {
+            'height': 0,
+            'hash': '0f9188f13cb7b2c71f2a335e3a4fc328bf5beb436012afca590b1a11466e2206',
+            'branchlen': 0,
+            'status': 'active',
+        } in self.nodes[2].getchaintips()
+
+        assert(len(self.nodes[2].getchaintips()) == 1)
+
+        self.log.info("Generate long chain for node0/node1")
+        self.generate(self.nodes[0], NODE2_BLOCKS_REQUIRED-self.nodes[0].getblockcount(), sync_fun=self.no_op)
+
+        self.log.info("Verify that node2 will sync the chain when it gets long enough")
+        self.sync_blocks()
+
+    def run_test(self):
+        self.test_chains_sync_when_long_enough()
+
+
+if __name__ == '__main__':
+    RejectLowDifficultyHeadersTest().main()
diff --git a/test/functional/test_runner.py b/test/functional/test_runner.py
index 37d0c4f87e2..b3492561986 100755
--- a/test/functional/test_runner.py
+++ b/test/functional/test_runner.py
@@ -186,6 +186,7 @@ BASE_SCRIPTS = [
     'wallet_signrawtransactionwithwallet.py --legacy-wallet',
     'wallet_signrawtransactionwithwallet.py --descriptors',
     'rpc_signrawtransactionwithkey.py',
+    'p2p_headers_sync_with_minchainwork.py',
     'rpc_rawtransaction.py --legacy-wallet',
     'wallet_groups.py --legacy-wallet',
     'wallet_transactiontime_rescan.py --descriptors',