diff --git a/test/functional/feature_proxy.py b/test/functional/feature_proxy.py
index 31d2ee8e1..5453f0be3 100755
--- a/test/functional/feature_proxy.py
+++ b/test/functional/feature_proxy.py
@@ -41,9 +41,11 @@ from test_framework.netutil import test_ipv6_local
 
 RANGE_BEGIN = PORT_MIN + 2 * PORT_RANGE  # Start after p2p and rpc ports
 
+
 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()
@@ -198,4 +200,3 @@ class ProxyTest(BitcoinTestFramework):
 
 if __name__ == '__main__':
     ProxyTest().main()
-
diff --git a/test/functional/mempool_accept.py b/test/functional/mempool_accept.py
index e2a219b85..efe720b9b 100755
--- a/test/functional/mempool_accept.py
+++ b/test/functional/mempool_accept.py
@@ -29,7 +29,6 @@ from test_framework.util import (
     assert_raises_rpc_error,
     bytes_to_hex_str,
     hex_str_to_bytes,
-    wait_until,
 )
 
 
@@ -38,7 +37,6 @@ class MempoolAcceptanceTest(BitcoinTestFramework):
         self.num_nodes = 1
         self.extra_args = [[
             '-txindex',
-            '-reindex',  # Need reindex for txindex
             '-acceptnonstdtxn=0',  # Try to mimic main-net
         ]] * self.num_nodes
 
@@ -56,7 +54,7 @@ class MempoolAcceptanceTest(BitcoinTestFramework):
 
         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/test_framework/test_framework.py b/test/functional/test_framework/test_framework.py
index 49c15112b..24e1a21a2 100755
--- a/test/functional/test_framework/test_framework.py
+++ b/test/functional/test_framework/test_framework.py
@@ -274,6 +274,17 @@ class BitcoinTestFramework(metaclass=BitcoinTestMetaClass):
         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)
+            self.log.debug('Generate a block with current time to finalize the cache and assert we are out of IBD')
+            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:
@@ -433,7 +444,7 @@ class BitcoinTestFramework(metaclass=BitcoinTestMetaClass):
     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
@@ -476,15 +487,24 @@ class BitcoinTestFramework(metaclass=BitcoinTestMetaClass):
             for node in self.nodes:
                 node.wait_for_rpc_connection()
 
-            # 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.
+            # 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(2):
                 for peer in range(4):
                     for j in range(25):
+                        if i == 1 and peer == 3 and j == 24:
+                            break
                         self.nodes[peer].generatetoaddress(1, self.nodes[peer].get_deterministic_priv_key().address)
                     # Must sync before next peer starts generating blocks
                     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 = []