diff --git a/test/functional/abc-miner-fund.py b/test/functional/abc-miner-fund.py
--- a/test/functional/abc-miner-fund.py
+++ b/test/functional/abc-miner-fund.py
@@ -3,7 +3,11 @@
 # Distributed under the MIT software license, see the accompanying
 # file COPYING or http://www.opensource.org/licenses/mit-license.php.
 
-from test_framework.blocktools import (create_block, create_coinbase)
+from test_framework.blocktools import (
+    create_block,
+    create_coinbase,
+    TIME_GENESIS_BLOCK,
+)
 from test_framework.messages import ToHex
 from test_framework.test_framework import BitcoinTestFramework
 from test_framework.util import (
@@ -26,6 +30,7 @@
 
 class MinerFundTest(BitcoinTestFramework):
     def set_test_params(self):
+        self.setup_clean_chain = True
         self.num_nodes = 1
         self.extra_args = [
             ['-enableminerfund', "-phononactivationtime={}".format(PHONON_ACTIVATION_TIME)]]
@@ -38,6 +43,14 @@
         node = self.nodes[0]
         address = node.get_deterministic_priv_key().address
 
+        self.log.info('Create some old blocks')
+        for t in range(TIME_GENESIS_BLOCK,
+                       TIME_GENESIS_BLOCK + 200 * 600, 600):
+            # ten-minute steps from genesis block time
+            self.nodes[0].setmocktime(t)
+            self.nodes[0].generatetoaddress(1, address)
+        assert_equal(self.nodes[0].getblockchaininfo()['blocks'], 200)
+
         # Get the vote started.
         node.setmocktime(1580000000)
 
diff --git a/test/functional/feature_proxy.py b/test/functional/feature_proxy.py
--- a/test/functional/feature_proxy.py
+++ b/test/functional/feature_proxy.py
@@ -50,6 +50,7 @@
 class ProxyTest(BitcoinTestFramework):
     def set_test_params(self):
         self.num_nodes = 4
+        self.setup_clean_chain = True
 
     def setup_nodes(self):
         self.have_ipv6 = test_ipv6_local()
diff --git a/test/functional/mempool_accept.py b/test/functional/mempool_accept.py
--- a/test/functional/mempool_accept.py
+++ b/test/functional/mempool_accept.py
@@ -25,7 +25,6 @@
 from test_framework.util import (
     assert_equal,
     assert_raises_rpc_error,
-    wait_until,
 )
 
 
@@ -34,7 +33,6 @@
         self.num_nodes = 1
         self.extra_args = [[
             '-txindex',
-            '-reindex',  # Need reindex for txindex
             '-acceptnonstdtxn=0',  # Try to mimic main-net
         ]] * self.num_nodes
 
@@ -53,7 +51,7 @@
 
         self.log.info('Start with empty mempool, and 200 blocks')
         self.mempool_size = 0
-        wait_until(lambda: node.getblockcount() == 200)
+        assert_equal(node.getblockcount(), 200)
         assert_equal(node.getmempoolinfo()['size'], self.mempool_size)
         coins = node.listunspent()
 
diff --git a/test/functional/rpc_blockchain.py b/test/functional/rpc_blockchain.py
--- a/test/functional/rpc_blockchain.py
+++ b/test/functional/rpc_blockchain.py
@@ -36,6 +36,7 @@
 from test_framework.blocktools import (
     create_block,
     create_coinbase,
+    TIME_GENESIS_BLOCK,
 )
 from test_framework.messages import (
     msg_block,
@@ -48,9 +49,12 @@
 class BlockchainTest(BitcoinTestFramework):
 
     def set_test_params(self):
+        self.setup_clean_chain = True
         self.num_nodes = 1
 
     def run_test(self):
+        self.mine_chain()
+
         # Set extra args with pruning after rescan is complete
         self.restart_node(0, extra_args=['-stopatheight=207', '-prune=1'])
 
@@ -66,6 +70,16 @@
             self._test_getblock()
         assert self.nodes[0].verifychain(4, 0)
 
+    def mine_chain(self):
+        self.log.info('Create some old blocks')
+        address = self.nodes[0].get_deterministic_priv_key().address
+        for t in range(TIME_GENESIS_BLOCK,
+                       TIME_GENESIS_BLOCK + 200 * 600, 600):
+            # ten-minute steps from genesis block time
+            self.nodes[0].setmocktime(t)
+            self.nodes[0].generatetoaddress(1, address)
+        assert_equal(self.nodes[0].getblockchaininfo()['blocks'], 200)
+
     def _test_getblockchaininfo(self):
         self.log.info("Test getblockchaininfo")
 
@@ -403,9 +417,11 @@
     def _test_getblock(self):
         # Checks for getblock verbose outputs
         node = self.nodes[0]
-        blockinfo = node.getblock(node.getblockhash(1), 2)
+        (blockhash, nextblockhash) = node.generate(2)
+
+        blockinfo = node.getblock(blockhash, 2)
         transactioninfo = node.gettransaction(blockinfo['tx'][0]['txid'])
-        blockheaderinfo = node.getblockheader(node.getblockhash(1), True)
+        blockheaderinfo = node.getblockheader(blockhash, True)
 
         assert_equal(blockinfo['hash'], transactioninfo['blockhash'])
         assert_equal(
@@ -429,6 +445,7 @@
         assert_equal(
             blockinfo['previousblockhash'],
             blockheaderinfo['previousblockhash'])
+        assert_equal(blockinfo['nextblockhash'], nextblockhash)
         assert_equal(
             blockinfo['nextblockhash'],
             blockheaderinfo['nextblockhash'])
diff --git a/test/functional/test_framework/test_framework.py b/test/functional/test_framework/test_framework.py
--- a/test/functional/test_framework/test_framework.py
+++ b/test/functional/test_framework/test_framework.py
@@ -30,7 +30,6 @@
     p2p_port,
     PortSeed,
     rpc_port,
-    set_node_times,
     sync_blocks,
     sync_mempools,
 )
@@ -79,7 +78,6 @@
         self.setup_clean_chain = False
         self.nodes = []
         self.network_thread = None
-        self.mocktime = 0
         # Wait for up to 60 seconds for the RPC server to respond
         self.rpc_timeout = 60
         self.supports_cli = False
@@ -259,6 +257,19 @@
         self.add_nodes(self.num_nodes, extra_args)
         self.start_nodes()
         self.import_deterministic_coinbase_privkeys()
+        if not self.setup_clean_chain:
+            for n in self.nodes:
+                assert_equal(n.getblockchaininfo()["blocks"], 199)
+            # To ensure that all nodes are out of IBD, the most recent block
+            # must have a timestamp not too old (see IsInitialBlockDownload()).
+            self.log.debug('Generate a block with current time')
+            block_hash = self.nodes[0].generate(1)[0]
+            block = self.nodes[0].getblock(blockhash=block_hash, verbosity=0)
+            for n in self.nodes:
+                n.submitblock(block)
+                chain_info = n.getblockchaininfo()
+                assert_equal(chain_info["blocks"], 200)
+                assert_equal(chain_info["initialblockdownload"], False)
 
     def import_deterministic_coinbase_privkeys(self):
         for n in self.nodes:
@@ -307,7 +318,6 @@
                 timewait=self.rpc_timeout,
                 bitcoind=binary[i],
                 bitcoin_cli=self.options.bitcoincli,
-                mocktime=self.mocktime,
                 coverage_dir=self.options.coveragedir,
                 extra_conf=extra_confs[i],
                 extra_args=extra_args[i],
@@ -436,7 +446,7 @@
     def _initialize_chain(self):
         """Initialize a pre-mined blockchain for use by the test.
 
-        Create a cache of a 200-block-long chain (with wallet) for MAX_NODES
+        Create a cache of a 199-block-long chain (with wallet) for MAX_NODES
         Afterward, create num_nodes copies from the cache."""
 
         assert self.num_nodes <= MAX_NODES
@@ -470,7 +480,6 @@
                     timewait=self.rpc_timeout,
                     bitcoind=self.options.bitcoind,
                     bitcoin_cli=self.options.bitcoincli,
-                    mocktime=self.mocktime,
                     coverage_dir=None,
                     emulator=self.options.emulator,
                 ))
@@ -489,33 +498,23 @@
             for node in self.nodes:
                 node.wait_for_rpc_connection()
 
-            # For backward compatibility of the python scripts with previous
-            # versions of the cache, set mocktime to Jan 1,
-            # 2014 + (201 * 10 * 60)
-            self.mocktime = 1388534400 + (201 * 10 * 60)
-
-            # Create a 200-block-long chain; each of the 4 first nodes
+            # Create a 199-block-long chain; each of the 4 first nodes
             # gets 25 mature blocks and 25 immature.
-            # Note: To preserve compatibility with older versions of
-            # initialize_chain, only 4 nodes will generate coins.
-            #
-            # blocks are created with timestamps 10 minutes apart
-            # starting from 2010 minutes in the past
-            block_time = self.mocktime - (201 * 10 * 60)
-            for i in range(2):
-                for peer in range(4):
-                    for j in range(25):
-                        set_node_times(self.nodes, block_time)
-                        self.nodes[peer].generatetoaddress(
-                            1, self.nodes[peer].get_deterministic_priv_key().address)
-                        block_time += 10 * 60
-                    # Must sync before next peer starts generating blocks
-                    sync_blocks(self.nodes)
+            # The 4th node gets only 24 immature blocks so that the very last
+            # block in the cache does not age too much (have an old tip age).
+            # This is needed so that we are out of IBD when the test starts,
+            # see the tip age check in IsInitialBlockDownload().
+            for i in range(8):
+                self.nodes[0].generatetoaddress(
+                    25 if i != 7 else 24, self.nodes[i % 4].get_deterministic_priv_key().address)
+            sync_blocks(self.nodes)
+
+            for n in self.nodes:
+                assert_equal(n.getblockchaininfo()["blocks"], 199)
 
             # Shut them down, and clean up cache directories:
             self.stop_nodes()
             self.nodes = []
-            self.mocktime = 0
 
             def cache_path(n, *paths):
                 return os.path.join(get_datadir_path(
diff --git a/test/functional/test_framework/test_node.py b/test/functional/test_framework/test_node.py
--- a/test/functional/test_framework/test_node.py
+++ b/test/functional/test_framework/test_node.py
@@ -58,7 +58,7 @@
     be dispatched to the RPC connection."""
 
     def __init__(self, i, datadir, *, chain, host, rpc_port, p2p_port, timewait, bitcoind, bitcoin_cli,
-                 mocktime, coverage_dir, extra_conf=None, extra_args=None, use_cli=False, emulator=None):
+                 coverage_dir, extra_conf=None, extra_args=None, use_cli=False, emulator=None):
         self.index = i
         self.datadir = datadir
         self.bitcoinconf = os.path.join(self.datadir, "bitcoin.conf")
@@ -90,7 +90,6 @@
             "-debug",
             "-debugexclude=libevent",
             "-debugexclude=leveldb",
-            "-mocktime=" + str(mocktime),
             "-uacomment=" + self.name,
             "-noprinttoconsole",
         ]
diff --git a/test/functional/wallet_create_tx.py b/test/functional/wallet_create_tx.py
--- a/test/functional/wallet_create_tx.py
+++ b/test/functional/wallet_create_tx.py
@@ -7,17 +7,25 @@
 from test_framework.util import (
     assert_equal,
 )
+from test_framework.blocktools import (
+    TIME_GENESIS_BLOCK,
+)
 
 
 class CreateTxWalletTest(BitcoinTestFramework):
     def set_test_params(self):
-        self.setup_clean_chain = False
+        self.setup_clean_chain = True
         self.num_nodes = 1
 
     def skip_test_if_missing_module(self):
         self.skip_if_no_wallet()
 
     def run_test(self):
+        self.log.info('Create some old blocks')
+        self.nodes[0].setmocktime(TIME_GENESIS_BLOCK)
+        self.nodes[0].generate(200)
+        self.nodes[0].setmocktime(0)
+
         self.log.info(
             'Check that we have some (old) blocks and that anti-fee-sniping is disabled')
         assert_equal(self.nodes[0].getblockchaininfo()['blocks'], 200)
diff --git a/test/functional/wallet_txn_doublespend.py b/test/functional/wallet_txn_doublespend.py
--- a/test/functional/wallet_txn_doublespend.py
+++ b/test/functional/wallet_txn_doublespend.py
@@ -36,6 +36,14 @@
     def run_test(self):
         # All nodes should start with 1,250 BCH:
         starting_balance = 1250
+
+        # All nodes should be out of IBD.
+        # If the nodes are not all out of IBD, that can interfere with
+        # blockchain sync later in the test when nodes are connected, due to
+        # timing issues.
+        for n in self.nodes:
+            assert n.getblockchaininfo()["initialblockdownload"] is False
+
         for i in range(4):
             assert_equal(self.nodes[i].getbalance(), starting_balance)
             # bug workaround, coins generated assigned to first getnewaddress!