diff --git a/test/functional/data/invalid_txs.py b/test/functional/data/invalid_txs.py
index 2e4ca83bf0f..d2d7202d860 100644
--- a/test/functional/data/invalid_txs.py
+++ b/test/functional/data/invalid_txs.py
@@ -263,6 +263,17 @@ def getDisabledOpcodeTemplate(opcode):
         'valid_in_block' : True
         })
 
+class NonStandardAndInvalid(BadTxTemplate):
+    """A non-standard transaction which is also consensus-invalid should return the consensus error."""
+    reject_reason = "mandatory-script-verify-flag-failed (OP_RETURN was encountered)"
+    expect_disconnect = True
+    valid_in_block = False
+
+    def get_tx(self):
+        return create_tx_with_script(
+            self.spend_tx, 0, script_sig=b'\x00' * 3 + b'\xab\x6a',
+            amount=(self.spend_avail // 2))
+
 # Disabled opcode tx templates (CVE-2010-5137)
 DisabledOpcodeTemplates = [getDisabledOpcodeTemplate(opcode) for opcode in [
     OP_CAT,
diff --git a/test/functional/feature_block.py b/test/functional/feature_block.py
index 384ca311c74..43bf61c174a 100755
--- a/test/functional/feature_block.py
+++ b/test/functional/feature_block.py
@@ -88,6 +88,7 @@ class FullBlockTest(BitcoinTestFramework):
         self.extra_args = [[
             '-acceptnonstdtxn=1',  # This is a consensus block test, we don't care about tx policy
             '-testactivationheight=bip34@2',
+            '-par=1', # Until https://github.com/bitcoin/bitcoin/issues/30960 is fixed
         ]]
 
     def run_test(self):
diff --git a/test/functional/p2p_invalid_tx.py b/test/functional/p2p_invalid_tx.py
index 241aefab245..ee8c6c16ca3 100755
--- a/test/functional/p2p_invalid_tx.py
+++ b/test/functional/p2p_invalid_tx.py
@@ -165,7 +165,7 @@ class InvalidTxRequestTest(BitcoinTestFramework):
             node.p2ps[0].send_txs_and_test([rejected_parent], node, success=False)
 
         self.log.info('Test that a peer disconnection causes erase its transactions from the orphan pool')
-        with node.assert_debug_log(['Erased 100 orphan transaction(s) from peer=25']):
+        with node.assert_debug_log(['Erased 100 orphan transaction(s) from peer=26']):
             self.reconnect_p2p(num_connections=1)
 
         self.log.info('Test that a transaction in the orphan pool is included in a new tip block causes erase this transaction from the orphan pool')