diff --git a/test/functional/p2p_segwit.py b/test/functional/p2p_segwit.py
index ade80429d9f13..b6360a3bb099f 100755
--- a/test/functional/p2p_segwit.py
+++ b/test/functional/p2p_segwit.py
@@ -47,7 +47,7 @@ def test_transaction_acceptance(rpc, p2p, tx, with_witness, accepted, reason=Non
         with mininode_lock:
             assert_equal(p2p.last_message["reject"].reason, reason)
 
-def test_witness_block(rpc, p2p, block, accepted, with_witness=True):
+def test_witness_block(rpc, p2p, block, accepted, with_witness=True, reason=None):
     """Send a block to the node and check that it's accepted
 
     - Submit the block over the p2p interface
@@ -58,6 +58,10 @@ def test_witness_block(rpc, p2p, block, accepted, with_witness=True):
         p2p.send_message(msg_block(block))
     p2p.sync_with_ping()
     assert_equal(rpc.getbestblockhash() == block.hash, accepted)
+    if (reason != None and not accepted):
+        # Check the rejection reason as well.
+        with mininode_lock:
+            assert_equal(p2p.last_message["reject"].reason, reason)
 
 class TestNode(P2PInterface):
     def __init__(self):
@@ -271,6 +275,80 @@ def test_unnecessary_witness_before_segwit_activation(self):
         self.utxo.pop(0)
         self.utxo.append(UTXO(tx4.sha256, 0, tx4.vout[0].nValue))
 
+    # ~6 months after segwit activation, the SCRIPT_VERIFY_WITNESS flag was
+    # backdated so that it applies to all blocks, going back to the genesis
+    # block.
+    #
+    # Consequently, version 0 witness outputs are never spendable without
+    # witness, and so can't be spent before segwit activation (the point at which
+    # blocks are permitted to contain witnesses).
+    def test_v0_outputs_arent_spendable(self):
+        self.log.info("Testing that v0 witness program outputs aren't spendable before activation")
+
+        assert len(self.utxo), "self.utxo is empty"
+
+        # Create two outputs, a p2wsh and p2sh-p2wsh
+        witness_program = CScript([OP_TRUE])
+        witness_hash = sha256(witness_program)
+        scriptPubKey = CScript([OP_0, witness_hash])
+
+        p2sh_pubkey = hash160(scriptPubKey)
+        p2sh_scriptPubKey = CScript([OP_HASH160, p2sh_pubkey, OP_EQUAL])
+
+        value = self.utxo[0].nValue // 3
+
+        tx = CTransaction()
+        tx.vin = [CTxIn(COutPoint(self.utxo[0].sha256, self.utxo[0].n), b'')]
+        tx.vout = [CTxOut(value, scriptPubKey), CTxOut(value, p2sh_scriptPubKey)]
+        tx.vout.append(CTxOut(value, CScript([OP_TRUE])))
+        tx.rehash()
+        txid = tx.sha256
+
+        # Add it to a block
+        block = self.build_next_block()
+        self.update_witness_block_with_transactions(block, [tx])
+        # Verify that segwit isn't activated. A block serialized with witness
+        # should be rejected prior to activation.
+        test_witness_block(self.nodes[0], self.test_node, block, accepted=False, with_witness=True, reason = b'unexpected-witness')
+        # Now send the block without witness. It should be accepted
+        test_witness_block(self.nodes[0], self.test_node, block, accepted=True, with_witness=False)
+
+        # Now try to spend the outputs. This should fail since SCRIPT_VERIFY_WITNESS is always enabled.
+        p2wsh_tx = CTransaction()
+        p2wsh_tx.vin = [CTxIn(COutPoint(txid, 0), b'')]
+        p2wsh_tx.vout = [CTxOut(value, CScript([OP_TRUE]))]
+        p2wsh_tx.wit.vtxinwit.append(CTxInWitness())
+        p2wsh_tx.wit.vtxinwit[0].scriptWitness.stack = [CScript([OP_TRUE])]
+        p2wsh_tx.rehash()
+
+        p2sh_p2wsh_tx = CTransaction()
+        p2sh_p2wsh_tx.vin = [CTxIn(COutPoint(txid, 1), CScript([scriptPubKey]))]
+        p2sh_p2wsh_tx.vout = [CTxOut(value, CScript([OP_TRUE]))]
+        p2sh_p2wsh_tx.wit.vtxinwit.append(CTxInWitness())
+        p2sh_p2wsh_tx.wit.vtxinwit[0].scriptWitness.stack = [CScript([OP_TRUE])]
+        p2sh_p2wsh_tx.rehash()
+
+        for tx in [p2wsh_tx, p2sh_p2wsh_tx]:
+
+            block = self.build_next_block()
+            self.update_witness_block_with_transactions(block, [tx])
+
+            # When the block is serialized with a witness, the block will be rejected because witness
+            # data isn't allowed in blocks that don't commit to witness data.
+            test_witness_block(self.nodes[0], self.test_node, block, accepted=False, with_witness=True, reason=b'unexpected-witness')
+
+            # When the block is serialized without witness, validation fails because the transaction is
+            # invalid (transactions are always validated with SCRIPT_VERIFY_WITNESS so a segwit v0 transaction
+            # without a witness is invalid).
+            # Note: The reject reason for this failure could be
+            # 'block-validation-failed' (if script check threads > 1) or
+            # 'non-mandatory-script-verify-flag (Witness program was passed an
+            # empty witness)' (otherwise).
+            # TODO: support multiple acceptable reject reasons.
+            test_witness_block(self.nodes[0], self.test_node, block, accepted=False, with_witness=False)
+
+        self.utxo.pop(0)
+        self.utxo.append(UTXO(txid, 2, value))
 
     # Mine enough blocks for segwit's vb state to be 'started'.
     def advance_to_segwit_started(self):
@@ -1476,9 +1554,10 @@ def test_p2sh_witness(self, segwit_activated):
         block = self.build_next_block()
         self.update_witness_block_with_transactions(block, [spend_tx])
 
-        # If we're before activation, then sending this without witnesses
-        # should be valid.  If we're after activation, then sending this with
-        # witnesses should be valid.
+        # If we're after activation, then sending this with witnesses should be valid.
+        # This no longer works before activation, because SCRIPT_VERIFY_WITNESS
+        # is always set.
+        # TODO: rewrite this test to make clear that it only works after activation.
         if segwit_activated:
             test_witness_block(self.nodes[0].rpc, self.test_node, block, accepted=True)
         else:
@@ -1897,6 +1976,7 @@ def run_test(self):
         self.test_witness_services() # Verifies NODE_WITNESS
         self.test_non_witness_transaction() # non-witness tx's are accepted
         self.test_unnecessary_witness_before_segwit_activation()
+        self.test_v0_outputs_arent_spendable()
         self.test_block_relay(segwit_activated=False)
 
         # Advance to segwit being 'started'