diff --git a/test/functional/abc-mempool-accept-txn.py b/test/functional/abc-mempool-accept-txn.py
--- a/test/functional/abc-mempool-accept-txn.py
+++ b/test/functional/abc-mempool-accept-txn.py
@@ -67,11 +67,6 @@
         self.tip = None
         self.blocks = {}
 
-    def setup_network(self):
-        self.extra_args = [['-norelaypriority']]
-        self.add_nodes(self.num_nodes, self.extra_args)
-        self.start_nodes()
-
     def add_options(self, parser):
         super().add_options(parser)
         parser.add_argument(
@@ -210,7 +205,7 @@
             spent_p2sh_tx = CTransaction()
             spent_p2sh_tx.vin.append(
                 CTxIn(COutPoint(p2sh_tx_to_spend.sha256, 0), b''))
-            spent_p2sh_tx.vout.append(CTxOut(1, output_script))
+            spent_p2sh_tx.vout.append(CTxOut(1000, output_script))
             # Sign the transaction using the redeem script
             sighash = SignatureHashForkId(
                 redeem_script, spent_p2sh_tx, 0, SIGHASH_ALL | SIGHASH_FORKID, p2sh_tx_to_spend.vout[0].nValue)
@@ -223,7 +218,7 @@
         # P2SH tests
         # Create a p2sh transaction
         p2sh_tx = self.create_and_sign_transaction(
-            out[0].tx, out[0].n, 1, p2sh_script)
+            out[0].tx, out[0].n, 10000, p2sh_script)
 
         # Add the transaction to the block
         block(1)
diff --git a/test/functional/abc-p2p-compactblocks.py b/test/functional/abc-p2p-compactblocks.py
--- a/test/functional/abc-p2p-compactblocks.py
+++ b/test/functional/abc-p2p-compactblocks.py
@@ -91,6 +91,8 @@
         self.tip = None
         self.blocks = {}
         self.excessive_block_size = 16 * ONE_MEGABYTE
+        # -norelaypriority is needed so that the invalidateblock at the end
+        # will insert free transactions back into the mempool.
         self.extra_args = [['-norelaypriority',
                             '-whitelist=127.0.0.1',
                             '-limitancestorcount=999999',
@@ -330,7 +332,8 @@
         assert cmpctblk_header.sha256 == b2.sha256
 
         # In order to avoid having to resend a ton of transactions, we invalidate
-        # b2, which will send all its transactions in the mempool.
+        # b2, which will send all its transactions in the mempool. Note that this
+        # assumes reorgs will insert low-fee transactions back into the mempool.
         node.invalidateblock(node.getbestblockhash())
 
         # Let's send a compact block and see if the node accepts it.
diff --git a/test/functional/abc-replay-protection.py b/test/functional/abc-replay-protection.py
--- a/test/functional/abc-replay-protection.py
+++ b/test/functional/abc-replay-protection.py
@@ -153,18 +153,18 @@
             # Fund transaction
             script = CScript([public_key, OP_CHECKSIG])
             txfund = create_transaction(
-                spend.tx, spend.n, b'', 50 * COIN, script)
+                spend.tx, spend.n, b'', 50 * COIN - 1000, script)
             txfund.rehash()
 
             # Spend transaction
             txspend = CTransaction()
-            txspend.vout.append(CTxOut(50 * COIN - 1000, CScript([OP_TRUE])))
+            txspend.vout.append(CTxOut(50 * COIN - 2000, CScript([OP_TRUE])))
             txspend.vin.append(CTxIn(COutPoint(txfund.sha256, 0), b''))
 
             # Sign the transaction
             sighashtype = (forkvalue << 8) | SIGHASH_ALL | SIGHASH_FORKID
             sighash = SignatureHashForkId(
-                script, txspend, 0, sighashtype, 50 * COIN)
+                script, txspend, 0, sighashtype, 50 * COIN - 1000)
             sig = private_key.sign(sighash) + \
                 bytes(bytearray([SIGHASH_ALL | SIGHASH_FORKID]))
             txspend.vin[0].scriptSig = CScript([sig])
diff --git a/test/functional/abc-rpc.py b/test/functional/abc-rpc.py
--- a/test/functional/abc-rpc.py
+++ b/test/functional/abc-rpc.py
@@ -22,8 +22,7 @@
         self.num_nodes = 1
         self.tip = None
         self.setup_clean_chain = True
-        self.extra_args = [['-norelaypriority',
-                            '-whitelist=127.0.0.1']]
+        self.extra_args = [['-whitelist=127.0.0.1']]
 
     def check_subversion(self, pattern_str):
         # Check that the subversion is set as expected
diff --git a/test/functional/abc-transaction-ordering.py b/test/functional/abc-transaction-ordering.py
--- a/test/functional/abc-transaction-ordering.py
+++ b/test/functional/abc-transaction-ordering.py
@@ -47,8 +47,7 @@
         self.block_heights = {}
         self.tip = None
         self.blocks = {}
-        self.extra_args = [['-whitelist=127.0.0.1',
-                            '-relaypriority=0']]
+        self.extra_args = [['-whitelist=127.0.0.1']]
 
     def add_transactions_to_block(self, block, tx_list):
         [tx.rehash() for tx in tx_list]