diff --git a/cardano_node_tests/tests/test_chain_transactions.py b/cardano_node_tests/tests/test_chain_transactions.py
index f0340f479..36806576b 100644
--- a/cardano_node_tests/tests/test_chain_transactions.py
+++ b/cardano_node_tests/tests/test_chain_transactions.py
@@ -11,6 +11,7 @@
 from cardano_node_tests.cluster_management import cluster_management
 from cardano_node_tests.tests import addrs_common
 from cardano_node_tests.tests import common
+from cardano_node_tests.tests import markers
 from cardano_node_tests.utils import configuration
 from cardano_node_tests.utils import dbsync_utils
 from cardano_node_tests.utils import helpers
@@ -97,11 +98,18 @@ def _repeat_submit(cluster_obj: clusterlib.ClusterLib, tx_file: pl.Path) -> str:
 class TestTxChaining:
     @pytest.fixture
     def cluster(self, cluster_manager: cluster_management.ClusterManager) -> clusterlib.ClusterLib:
+        """Lock the whole cluster instance.
+
+        The test checks how many blocks the chained Txs take, so Txs of other tests must not
+        take the block space. The Txs also fill the mempool, which would slow down the
+        submission of Txs of other tests.
+        """
         return cluster_manager.get(
-            lock_resources=[cluster_management.Resources.PERF],
+            lock_resources=[cluster_management.Resources.CLUSTER],
         )
 
     @allure.link(helpers.get_vcs_link())
+    @pytest.mark.xdist_split(markers.XdSplits.heavy)
     @pytest.mark.dbsync
     def test_tx_chaining(
         self,
diff --git a/cardano_node_tests/tests/test_env_network_id.py b/cardano_node_tests/tests/test_env_network_id.py
index 4c80c4d00..003efa410 100644
--- a/cardano_node_tests/tests/test_env_network_id.py
+++ b/cardano_node_tests/tests/test_env_network_id.py
@@ -4,7 +4,6 @@
 import os
 import re
 import time
-import typing as tp
 
 import allure
 import pytest
@@ -82,16 +81,14 @@ def skip_on_no_env(
 @pytest.fixture
 def set_network_id_env(
     cluster: clusterlib.ClusterLib,
-) -> tp.Generator[None]:
-    """Set `CARDANO_NODE_NETWORK_ID` and prevent `cardano-cli` from using `--testnet-magic`."""
-    magic_args = cluster.magic_args[:]
-
-    os.environ["CARDANO_NODE_NETWORK_ID"] = str(cluster.network_magic)
-    cluster.magic_args = []
-    yield
-    if os.environ.get("CARDANO_NODE_NETWORK_ID"):
-        del os.environ["CARDANO_NODE_NETWORK_ID"]
-    cluster.magic_args = magic_args
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """Set `CARDANO_NODE_NETWORK_ID` and prevent `cardano-cli` from using `--testnet-magic`.
+
+    The original values are restored after the test, also when the test changed them.
+    """
+    monkeypatch.setenv("CARDANO_NODE_NETWORK_ID", str(cluster.network_magic))
+    monkeypatch.setattr(cluster, "magic_args", [])
 
 
 @pytest.fixture
diff --git a/cardano_node_tests/tests/test_kes.py b/cardano_node_tests/tests/test_kes.py
index e16bcf22b..4fbcfd9d8 100644
--- a/cardano_node_tests/tests/test_kes.py
+++ b/cardano_node_tests/tests/test_kes.py
@@ -772,7 +772,7 @@ def test_update_valid_opcert(
     @allure.link(helpers.get_vcs_link())
     def test_no_kes_period_arg(
         self,
-        cluster: clusterlib.ClusterLib,
+        cluster_use_pool: tuple[clusterlib.ClusterLib, str],
         cluster_manager: cluster_management.ClusterManager,
     ):
         """Try to generate new operational certificate without specifying the `--kes-period`.
@@ -780,17 +780,22 @@ def test_no_kes_period_arg(
         Test that operational certificate generation fails when required `--kes-period` argument
         is not provided. Expect failure.
 
-        * Get pool KES verification key, cold signing key, and counter file from pool2
+        * Get pool KES verification key, cold signing key, and a copy of counter file
         * Attempt to execute `cardano-cli node issue-op-cert` without --kes-period argument
         * Check that command fails with "Missing: --kes-period NATURAL" error
         * Verify operational certificate file was not created
         """
-        pool_name = cluster_management.Resources.POOL2
+        cluster, pool_name = cluster_use_pool
         pool_rec = cluster_manager.cache.addrs_data[pool_name]
 
         temp_template = common.get_test_id(cluster)
         out_file = pl.Path(f"{temp_template}_shouldnt_exist.opcert")
 
+        # The command would increment the counter if it succeeded, so don't pass it the shared
+        # counter file of the cluster pool
+        counter_file = pl.Path(f"{temp_template}_cold.counter")
+        shutil.copyfile(pool_rec["cold_key_pair"].counter_file, counter_file)
+
         # Try to generate new operational certificate without specifying the `--kes-period`
         with pytest.raises(clusterlib.CLIError) as excinfo:
             cluster.cli(
@@ -802,7 +807,7 @@ def test_no_kes_period_arg(
                     "--cold-signing-key-file",
                     str(pool_rec["cold_key_pair"].skey_file),
                     "--operational-certificate-issue-counter",
-                    str(pool_rec["cold_key_pair"].counter_file),
+                    str(counter_file),
                     "--out-file",
                     str(out_file),
                 ]
@@ -817,7 +822,7 @@ def test_no_kes_period_arg(
     @pytest.mark.smoke
     def test_negative_kes_period_arg(
         self,
-        cluster: clusterlib.ClusterLib,
+        cluster_use_pool: tuple[clusterlib.ClusterLib, str],
         cluster_manager: cluster_management.ClusterManager,
     ):
         """Try to generate new operational certificate with a negative value for `--kes-period`.
@@ -825,17 +830,22 @@ def test_negative_kes_period_arg(
         Test that operational certificate generation fails when --kes-period is set to a
         negative value. Expect failure.
 
-        * Get pool KES verification key, cold signing key, and counter file from pool2
+        * Get pool KES verification key, cold signing key, and a copy of counter file
         * Attempt to generate operational certificate with --kes-period set to -100
         * Check that generation fails with "KES_PERIOD must not be less than 0" error
         """
-        common.get_test_id(cluster)
+        cluster, pool_name = cluster_use_pool
+        temp_template = common.get_test_id(cluster)
 
-        pool_name = cluster_management.Resources.POOL2
         pool_rec = cluster_manager.cache.addrs_data[pool_name]
 
         node_name = pool_name.replace("node-", "")
 
+        # The command would increment the counter if it succeeded, so don't pass it the shared
+        # counter file of the cluster pool
+        counter_file = pl.Path(f"{temp_template}_cold.counter")
+        shutil.copyfile(pool_rec["cold_key_pair"].counter_file, counter_file)
+
         # Generate new operational certificate with negative value for `--kes-period`
         invalid_kes_period = -100
 
@@ -844,7 +854,7 @@ def test_negative_kes_period_arg(
                 node_name=f"{node_name}_invalid_opcert_file",
                 kes_vkey_file=pool_rec["kes_key_pair"].vkey_file,
                 cold_skey_file=pool_rec["cold_key_pair"].skey_file,
-                cold_counter_file=pool_rec["cold_key_pair"].counter_file,
+                cold_counter_file=counter_file,
                 kes_period=invalid_kes_period,
             )
         except clusterlib.CLIError as exc:
diff --git a/cardano_node_tests/tests/test_rollback.py b/cardano_node_tests/tests/test_rollback.py
index 6eb5926cc..f0fde6871 100644
--- a/cardano_node_tests/tests/test_rollback.py
+++ b/cardano_node_tests/tests/test_rollback.py
@@ -399,12 +399,13 @@ def test_permanent_fork(
         split_block = cluster.g_query.get_block_no() + 10
         final_block = split_block + cluster.genesis["securityParam"]
 
+        # The cluster needs respin after this point. Request the respin before the split, so
+        # it is requested even when the split fails half-way.
+        cluster_manager.set_needs_respin()
+
         # Split the cluster into two separate clusters
         self.split_cluster(split_topology_dir=split_topology_dir)
 
-        # The cluster needs respin after this point
-        cluster_manager.set_needs_respin()
-
         # Submit a Tx number 2 on the first cluster
         tx_outputs.append(
             self.node_submit_tx(
diff --git a/cardano_node_tests/tests/tests_dijkstra/test_bls_rotation.py b/cardano_node_tests/tests/tests_dijkstra/test_bls_rotation.py
index 885b31ed1..d7f48ea08 100644
--- a/cardano_node_tests/tests/tests_dijkstra/test_bls_rotation.py
+++ b/cardano_node_tests/tests/tests_dijkstra/test_bls_rotation.py
@@ -188,6 +188,10 @@ def cluster_leios_singleton(
             f"the {epoch_tail_sec} sec search window"
         )
 
+    # The test waits for up to 6.5 epochs: up to `leios.VOTING_START_EPOCH` epochs, then
+    # `bls.BLS_ACTIVATION_EPOCHS` epochs, and ~20 min of log searches and node restarts
+    common.skip_on_long_epochs(cluster_obj=cluster_obj, epochs=6.5)
+
     cluster_manager.set_needs_respin()
     return cluster_obj
 
@@ -1258,9 +1262,6 @@ def test_rotation_pair_keeps_voting(
           the rotation is seated - and check that the pool votes again
         """
         cluster = cluster_leios_singleton
-        # Waits for up to 6.5 epochs: up to `leios.VOTING_START_EPOCH` epochs, then
-        # `bls.BLS_ACTIVATION_EPOCHS` epochs, and ~20 min of log searches and node restarts
-        common.skip_on_long_epochs(cluster_obj=cluster, epochs=6.5)
         temp_template = common.get_test_id(cluster)
 
         pool_name = cluster_management.Resources.POOL_FOR_OFFLINE
diff --git a/cardano_node_tests/tests/tests_plutus/test_delegation.py b/cardano_node_tests/tests/tests_plutus/test_delegation.py
index 590603986..6d75e3947 100644
--- a/cardano_node_tests/tests/tests_plutus/test_delegation.py
+++ b/cardano_node_tests/tests/tests_plutus/test_delegation.py
@@ -44,11 +44,15 @@
 @pytest.fixture
 def cluster_lock_42stake(
     cluster_manager: cluster_management.ClusterManager,
-) -> tuple[clusterlib.ClusterLib, str]:
+) -> tp.Generator[tuple[clusterlib.ClusterLib, str]]:
     """Make sure just one staking Plutus test run at a time.
 
     Plutus script always has the same address. When one script is used in multiple
     tests that are running in parallel, the balances etc. don't add up.
+
+    When a test fails before deregistering the Plutus script stake address, the address
+    stays registered and all the following tests using the script would be skipped.
+    Respin the cluster instance in such case.
     """
     plutus_script = (
         plutus_common.STAKE_PLUTUS_V2
@@ -72,7 +76,14 @@ def cluster_lock_42stake(
         addrs_data=cluster_manager.cache.addrs_data,
         pool_name=pool_name,
     )
-    return cluster_obj, pool_id
+    yield cluster_obj, pool_id
+
+    script_stake_address = cluster_obj.g_stake_address.gen_stake_addr(
+        addr_name=f"script_stake_check_{clusterlib.get_rand_str(4)}",
+        stake_script_file=plutus_script,
+    )
+    if cluster_obj.g_query.get_stake_addr_info(script_stake_address):
+        cluster_manager.set_needs_respin()
 
 
 @pytest.fixture