diff --git a/test/functional/replace-by-fee.py b/test/functional/replace-by-fee.py
index 269d57775..815e96484 100755
--- a/test/functional/replace-by-fee.py
+++ b/test/functional/replace-by-fee.py
@@ -72,8 +72,14 @@ class ReplaceByFeeTest(BitcoinTestFramework):
                            ["-mempoolreplacement=0"]]
 
     def run_test(self):
+        # Leave IBD
+        self.nodes[0].generate(1)
+
         make_utxo(self.nodes[0], 1*COIN)
 
+        # Ensure nodes are synced
+        self.sync_all()
+
         self.log.info("Running test simple doublespend...")
         self.test_simple_doublespend()
 
@@ -110,13 +116,18 @@ class ReplaceByFeeTest(BitcoinTestFramework):
         """Simple doublespend"""
         tx0_outpoint = make_utxo(self.nodes[0], int(1.1*COIN))
 
+        # make_utxo may have generated a bunch of blocks, so we need to sync
+        # before we can spend the coins generated, or else the resulting
+        # transactions might not be accepted by our peers.
+        self.sync_all()
+
         tx1a = CTransaction()
         tx1a.vin = [CTxIn(tx0_outpoint, nSequence=0)]
         tx1a.vout = [CTxOut(1*COIN, CScript([b'a']))]
         tx1a_hex = txToHex(tx1a)
         tx1a_txid = self.nodes[0].sendrawtransaction(tx1a_hex, True)
 
-        self.sync_all([self.nodes])
+        self.sync_all()
 
         # Should fail because we haven't changed the fee
         tx1b = CTransaction()
diff --git a/test/functional/sendheaders.py b/test/functional/sendheaders.py
index fe577dc20..60d107b24 100755
--- a/test/functional/sendheaders.py
+++ b/test/functional/sendheaders.py
@@ -225,6 +225,10 @@ class SendHeadersTest(BitcoinTestFramework):
         inv_node.wait_for_verack()
         test_node.wait_for_verack()
 
+        # Ensure verack's have been processed by our peer
+        inv_node.sync_with_ping()
+        test_node.sync_with_ping()
+
         tip = int(self.nodes[0].getbestblockhash(), 16)
 
         # PART 1