diff --git a/test/functional/data/blockheader_testnet3.hex b/test/functional/data/blockheader_testnet3.hex
new file mode 100644
--- /dev/null
+++ b/test/functional/data/blockheader_testnet3.hex
@@ -0,0 +1,548 @@
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diff --git a/test/functional/p2p_dos_header_tree.py b/test/functional/p2p_dos_header_tree.py
new file mode 100755
--- /dev/null
+++ b/test/functional/p2p_dos_header_tree.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+# Copyright (c) 2019 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.messages import (
+    CBlockHeader,
+    FromHex,
+)
+from test_framework.mininode import (
+    P2PInterface,
+    msg_headers,
+)
+from test_framework.test_framework import BitcoinTestFramework
+
+import os
+
+
+class RejectLowDifficultyHeadersTest(BitcoinTestFramework):
+    def set_test_params(self):
+        self.setup_clean_chain = True
+        self.chain = 'testnet3'  # Use testnet chain because it has an early checkpoint
+        self.num_nodes = 2
+
+    def add_options(self, parser):
+        parser.add_argument(
+            '--datafile',
+            default='data/blockheader_testnet3.hex',
+            help='Test data file (default: %(default)s)',
+        )
+
+    def run_test(self):
+        self.log.info("Read headers data")
+        self.headers_file_path = os.path.join(
+            os.path.dirname(
+                os.path.realpath(__file__)),
+            self.options.datafile)
+        with open(self.headers_file_path, encoding='utf-8') as headers_data:
+            h_lines = [line.strip() for line in headers_data.readlines()]
+
+        # The headers data is taken from testnet3 for early blocks from genesis until the first checkpoint. There are
+        # two headers with valid POW at height 1 and 2, forking off from
+        # genesis. They are indicated by the FORK_PREFIX.
+        FORK_PREFIX = 'fork:'
+        self.headers = [
+            line for line in h_lines if not line.startswith(FORK_PREFIX)]
+        self.headers_fork = [line[len(FORK_PREFIX):]
+                             for line in h_lines if line.startswith(FORK_PREFIX)]
+
+        self.headers = [FromHex(CBlockHeader(), h) for h in self.headers]
+        self.headers_fork = [FromHex(CBlockHeader(), h)
+                             for h in self.headers_fork]
+
+        self.log.info(
+            "Feed all non-fork headers, including and up to the first checkpoint")
+        self.nodes[0].add_p2p_connection(P2PInterface())
+        self.nodes[0].p2p.send_message(msg_headers(self.headers))
+        self.nodes[0].p2p.sync_with_ping()
+        assert {
+            'height': 546,
+            'hash': '000000002a936ca763904c3c35fce2f3556c559c0214345d31b1bcebf76acb70',
+            'branchlen': 546,
+            'status': 'headers-only',
+        } in self.nodes[0].getchaintips()
+
+        self.log.info("Feed all fork headers (fails due to checkpoint)")
+        with self.nodes[0].assert_debug_log(['bad-fork-prior-to-checkpoint (code 67)']):
+            self.nodes[0].p2p.send_message(msg_headers(self.headers_fork))
+            self.nodes[0].p2p.wait_for_disconnect()
+
+        self.log.info("Feed all fork headers (succeeds without checkpoint)")
+        # On node 0 it succeeds because checkpoints are disabled
+        self.restart_node(0, extra_args=['-nocheckpoints'])
+        self.nodes[0].add_p2p_connection(P2PInterface())
+        self.nodes[0].p2p.send_message(msg_headers(self.headers_fork))
+        self.nodes[0].p2p.sync_with_ping()
+        assert {
+            "height": 2,
+            "hash": "00000000b0494bd6c3d5ff79c497cfce40831871cbf39b1bc28bd1dac817dc39",
+            "branchlen": 2,
+            "status": "headers-only",
+        } in self.nodes[0].getchaintips()
+
+        # On node 1 it succeeds because no checkpoint has been reached yet by a
+        # chain tip
+        self.nodes[1].add_p2p_connection(P2PInterface())
+        self.nodes[1].p2p.send_message(msg_headers(self.headers_fork))
+        self.nodes[1].p2p.sync_with_ping()
+        assert {
+            "height": 2,
+            "hash": "00000000b0494bd6c3d5ff79c497cfce40831871cbf39b1bc28bd1dac817dc39",
+            "branchlen": 2,
+            "status": "headers-only",
+        } in self.nodes[1].getchaintips()
+
+
+if __name__ == '__main__':
+    RejectLowDifficultyHeadersTest().main()