diff --git a/tests/test_connection.py b/tests/test_connection.py
index 141aa5b4e..4ca2b60a6 100644
--- a/tests/test_connection.py
+++ b/tests/test_connection.py
@@ -134,6 +134,7 @@ def test_bad_opening(node_factory):
 
 
 @unittest.skipIf(not DEVELOPER, "gossip without DEVELOPER=1 is slow")
+@unittest.skipIf(TEST_NETWORK != 'regtest', "Fee computation and limits are network specific")
 def test_opening_tiny_channel(node_factory):
     # Test custom min-capacity-sat parameters
     #
@@ -1959,11 +1960,12 @@ def test_change_chaining(node_factory, bitcoind):
     l1.rpc.fundchannel(l3.info['id'], 10**7, minconf=0)
 
 
-def test_feerate_spam(node_factory):
+def test_feerate_spam(node_factory, chainparams):
     l1, l2 = node_factory.line_graph(2)
 
+    slack = 25000000 if not chainparams['elements'] else 35000000
     # Pay almost everything to l2.
-    l1.pay(l2, 10**9 - 25000000)
+    l1.pay(l2, 10**9 - slack)
 
     # It will send this once (may have happened before line_graph's wait)
     wait_for(lambda: l1.daemon.is_in_log('Setting REMOTE feerate to 15000'))
diff --git a/tests/test_db.py b/tests/test_db.py
index c89d5ac00..e45af3f08 100644
--- a/tests/test_db.py
+++ b/tests/test_db.py
@@ -23,7 +23,8 @@ def test_db_dangling_peer_fix(node_factory):
     l2.fund_channel(l1, 200000, wait_for_active=True)
 
 
-def test_block_backfill(node_factory, bitcoind):
+@unittest.skipIf(TEST_NETWORK != 'regtest', "Address is network specific")
+def test_block_backfill(node_factory, bitcoind, chainparams):
     """Test whether we backfill data from the blockchain correctly.
 
     For normal operation we will process any block after the initial start
@@ -120,6 +121,7 @@ def test_max_channel_id(node_factory, bitcoind):
 
 @unittest.skipIf(not COMPAT, "needs COMPAT to convert obsolete db")
 @unittest.skipIf(os.getenv('TEST_DB_PROVIDER', 'sqlite3') != 'sqlite3', "This test is based on a sqlite3 snapshot")
+@unittest.skipIf(TEST_NETWORK != 'regtest', "The network must match the DB snapshot")
 def test_scid_upgrade(node_factory):
 
     # Created through the power of sed "s/X'\([0-9]*\)78\([0-9]*\)78\([0-9]*\)'/X'\13A\23A\3'/"
diff --git a/tests/test_gossip.py b/tests/test_gossip.py
index 19d5d760d..d0fd1beeb 100644
--- a/tests/test_gossip.py
+++ b/tests/test_gossip.py
@@ -1,5 +1,6 @@
 from collections import Counter
 from fixtures import *  # noqa: F401,F403
+from fixtures import TEST_NETWORK
 from lightning import RpcError
 from utils import wait_for, TIMEOUT, only_one, sync_blockheight
 
@@ -1508,6 +1509,7 @@ def test_gossip_no_backtalk(node_factory):
 
 
 @unittest.skipIf(not DEVELOPER, "Needs --dev-gossip")
+@unittest.skipIf(TEST_NETWORK != 'regtest', "Channel announcement contains genesis hash, receiving node discards on mismatch")
 def test_gossip_ratelimit(node_factory):
     # These make the channel exist, but we use our own gossip.
     l1, l2 = node_factory.line_graph(2, wait_for_announce=True)
diff --git a/tests/test_invoices.py b/tests/test_invoices.py
index fca783ea9..f64c40deb 100644
--- a/tests/test_invoices.py
+++ b/tests/test_invoices.py
@@ -1,4 +1,5 @@
 from fixtures import *  # noqa: F401,F403
+from fixtures import TEST_NETWORK
 from lightning import RpcError
 from utils import only_one, DEVELOPER, wait_for, wait_channel_quiescent
 
@@ -123,6 +124,7 @@ def test_invoice_preimage(node_factory):
 
 
 @unittest.skipIf(not DEVELOPER, "gossip without DEVELOPER=1 is slow")
+@unittest.skipIf(TEST_NETWORK != 'regtest', "Amounts too low, dominated by fees in elements")
 def test_invoice_routeboost(node_factory, bitcoind):
     """Test routeboost 'r' hint in bolt11 invoice.
     """
diff --git a/tests/test_misc.py b/tests/test_misc.py
index 7cc5bb815..6b0718581 100644
--- a/tests/test_misc.py
+++ b/tests/test_misc.py
@@ -1,6 +1,7 @@
 from bitcoin.rpc import RawProxy
 from decimal import Decimal
 from fixtures import *  # noqa: F401,F403
+from fixtures import TEST_NETWORK
 from flaky import flaky  # noqa: F401
 from lightning import RpcError
 from threading import Event
diff --git a/tests/test_pay.py b/tests/test_pay.py
index 1810c42ee..404a08a40 100644
--- a/tests/test_pay.py
+++ b/tests/test_pay.py
@@ -1,4 +1,5 @@
 from fixtures import *  # noqa: F401,F403
+from fixtures import TEST_NETWORK
 from flaky import flaky  # noqa: F401
 from lightning import RpcError, Millisatoshi
 from utils import DEVELOPER, wait_for, only_one, sync_blockheight, SLOW_MACHINE, TIMEOUT, VALGRIND
@@ -560,6 +561,7 @@ def test_sendpay(node_factory):
     assert payments[0]['payment_preimage'] == preimage3
 
 
+@unittest.skipIf(TEST_NETWORK != 'regtest', "The reserve computation is bitcoin specific")
 def test_sendpay_cant_afford(node_factory):
     l1, l2 = node_factory.line_graph(2, fundamount=10**6)
 
@@ -2251,6 +2253,7 @@ def test_channel_spendable_capped(node_factory, bitcoind):
     assert l1.rpc.listpeers()['peers'][0]['channels'][0]['spendable_msat'] == Millisatoshi(0xFFFFFFFF)
 
 
+@unittest.skipIf(TEST_NETWORK != 'regtest', 'The numbers below are bitcoin specific')
 def test_channel_drainage(node_factory, bitcoind):
     """Test channel drainage.