diff --git a/test/functional/rpc_preciousblock.py b/test/functional/rpc_preciousblock.py
--- a/test/functional/rpc_preciousblock.py
+++ b/test/functional/rpc_preciousblock.py
@@ -11,7 +11,6 @@
 from test_framework.util import (
     assert_equal,
     connect_nodes_bi,
-    sync_chain,
     sync_blocks,
 )
 
@@ -83,8 +82,8 @@
         assert_equal(self.nodes[0].getbestblockhash(), hashC)
         self.log.info("Make Node1 prefer block C")
         self.nodes[1].preciousblock(hashC)
-        sync_chain(self.nodes[0:2])
         # wait because node 1 may not have downloaded hashC
+        sync_blocks(self.nodes[0:2])
         assert_equal(self.nodes[1].getbestblockhash(), hashC)
         self.log.info("Make Node1 prefer block G again")
         self.nodes[1].preciousblock(hashG)
diff --git a/test/functional/test_framework/util.py b/test/functional/test_framework/util.py
--- a/test/functional/test_framework/util.py
+++ b/test/functional/test_framework/util.py
@@ -418,36 +418,14 @@
     one node already synced to the latest, stable tip, otherwise there's a
     chance it might return before all nodes are stably synced.
     """
-    # Use getblockcount() instead of waitforblockheight() to determine the
-    # initial max height because the two RPCs look at different internal global
-    # variables (chainActive vs latestBlock) and the former gets updated
-    # earlier.
-    maxheight = max(x.getblockcount() for x in rpc_connections)
-    start_time = cur_time = time.time()
-    while cur_time <= start_time + timeout:
-        tips = [r.waitforblockheight(maxheight, int(wait * 1000))
-                for r in rpc_connections]
-        if all(t["height"] == maxheight for t in tips):
-            if all(t["hash"] == tips[0]["hash"] for t in tips):
-                return
-            raise AssertionError("Block sync failed, mismatched block hashes:{}".format(
-                                 "".join("\n  {!r}".format(tip) for tip in tips)))
-        cur_time = time.time()
-    raise AssertionError("Block sync to height {} timed out:{}".format(
-                         maxheight, "".join("\n  {!r}".format(tip) for tip in tips)))
-
-
-def sync_chain(rpc_connections, *, wait=1, timeout=60):
-    """
-    Wait until everybody has the same best block
-    """
-    while timeout > 0:
+    stop_time = time.time() + timeout
+    while time.time() <= stop_time:
         best_hash = [x.getbestblockhash() for x in rpc_connections]
-        if best_hash == [best_hash[0]] * len(best_hash):
+        if best_hash.count(best_hash[0]) == len(rpc_connections):
             return
         time.sleep(wait)
-        timeout -= wait
-    raise AssertionError("Chain sync failed: Best block hashes don't match")
+    raise AssertionError("Block sync timed out:{}".format(
+        "".join("\n  {!r}".format(b) for b in best_hash)))
 
 
 def sync_mempools(rpc_connections, *, wait=1, timeout=60, flush_scheduler=True):
@@ -455,20 +433,17 @@
     Wait until everybody has the same transactions in their memory
     pools
     """
-    while timeout > 0:
-        pool = set(rpc_connections[0].getrawmempool())
-        num_match = 1
-        for i in range(1, len(rpc_connections)):
-            if set(rpc_connections[i].getrawmempool()) == pool:
-                num_match = num_match + 1
-        if num_match == len(rpc_connections):
+    stop_time = time.time() + timeout
+    while time.time() <= stop_time:
+        pool = [set(r.getrawmempool()) for r in rpc_connections]
+        if pool.count(pool[0]) == len(rpc_connections):
             if flush_scheduler:
                 for r in rpc_connections:
                     r.syncwithvalidationinterfacequeue()
             return
         time.sleep(wait)
-        timeout -= wait
-    raise AssertionError("Mempool sync failed")
+    raise AssertionError("Mempool sync timed out:{}".format(
+        "".join("\n  {!r}".format(m) for m in pool)))
 
 # Transaction/Block functions
 #############################