diff --git a/cardano_node_tests/tests/plutus_common.py b/cardano_node_tests/tests/plutus_common.py
index b7280b6a4..6f628d71e 100644
--- a/cardano_node_tests/tests/plutus_common.py
+++ b/cardano_node_tests/tests/plutus_common.py
@@ -304,6 +304,33 @@ class PlutusScriptData:
 )
 
 
+# Slots between the tip and the end of the validity interval of a transaction that runs
+# a "time range" script. Long enough for the transaction to get submitted and land in a
+# block, and capped by `get_timerange_slots_offset`.
+TIMERANGE_SLOTS_OFFSET = 300
+
+
+def get_timerange_slots_offset(*, cluster_obj: clusterlib.ClusterLib) -> int:
+    """Return the slot offset to use for the validity interval of a "time range" script.
+
+    A script that looks at the transaction validity interval makes the ledger translate
+    the end of the interval to a time, which it can do only up to its forecast horizon:
+    the end of the first epoch that starts at or after the stability window from the tip.
+    An interval reaching past that fails the script with `TimeTranslationPastHorizon`, so
+    `TIMERANGE_SLOTS_OFFSET` is capped with the stability window, which is by definition
+    always inside the horizon.
+
+    Args:
+        cluster_obj: An instance of `clusterlib.ClusterLib`.
+
+    Returns:
+        int: The number of slots to set the validity interval to, counted from the tip.
+    """
+    return min(
+        TIMERANGE_SLOTS_OFFSET, clusterlib_utils.get_stability_window(cluster_obj=cluster_obj)
+    )
+
+
 def rotate_shift_bitwise_fails(protocol_version: int) -> bool:
     """Check if the rotate/shift bitwise builtin scripts fail on the given protocol version.
 
diff --git a/cardano_node_tests/tests/tests_plutus/test_mint_build.py b/cardano_node_tests/tests/tests_plutus/test_mint_build.py
index 61249be88..2735407ab 100644
--- a/cardano_node_tests/tests/tests_plutus/test_mint_build.py
+++ b/cardano_node_tests/tests/tests_plutus/test_mint_build.py
@@ -405,7 +405,7 @@ def test_time_range_minting(
         # Step 2: mint the "qacoin"
 
         slot_step2 = cluster.g_query.get_slot_no()
-        slots_offset = 300
+        slots_offset = plutus_common.get_timerange_slots_offset(cluster_obj=cluster)
         timestamp_offset_ms = int(slots_offset * cluster.slot_length + 5) * 1_000
 
         # POSIX timestamp + offset
@@ -653,7 +653,7 @@ def test_two_scripts_minting(
         ]
 
         # "time range" qacoin
-        slots_offset = 300
+        slots_offset = plutus_common.get_timerange_slots_offset(cluster_obj=cluster)
         timestamp_offset_ms = int(slots_offset * cluster.slot_length + 5) * 1_000
 
         # POSIX timestamp + offset
@@ -997,10 +997,7 @@ def test_ttl_horizon(
             *mint_txouts,
         ]
 
-        # Calculate 3k/f
-        offset_3kf = round(
-            3 * cluster.genesis["securityParam"] / cluster.genesis["activeSlotsCoeff"]
-        )
+        offset_3kf = clusterlib_utils.get_stability_window(cluster_obj=cluster)
 
         # Use 3k/f + `epoch_length` slots for ttl - this will not meet the `expect_pass` condition
         if ttl_offset == -1:
diff --git a/cardano_node_tests/tests/tests_plutus/test_mint_raw.py b/cardano_node_tests/tests/tests_plutus/test_mint_raw.py
index f31475b38..f13a39871 100644
--- a/cardano_node_tests/tests/tests_plutus/test_mint_raw.py
+++ b/cardano_node_tests/tests/tests_plutus/test_mint_raw.py
@@ -14,6 +14,7 @@
 from cardano_node_tests.tests import common
 from cardano_node_tests.tests import plutus_common
 from cardano_node_tests.tests.tests_plutus import mint_raw
+from cardano_node_tests.utils import clusterlib_utils
 from cardano_node_tests.utils import dbsync_utils
 from cardano_node_tests.utils import helpers
 from cardano_node_tests.utils import tx_view
@@ -422,7 +423,7 @@ def test_time_range_minting(
         # Step 2: mint the "qacoin"
 
         slot_step2 = cluster.g_query.get_slot_no()
-        slots_offset = 300
+        slots_offset = plutus_common.get_timerange_slots_offset(cluster_obj=cluster)
         timestamp_offset_ms = int(slots_offset * cluster.slot_length + 5) * 1_000
 
         # POSIX timestamp + offset
@@ -625,7 +626,7 @@ def test_two_scripts_minting(
         ]
 
         # "timerange" qacoin
-        slots_offset = 300
+        slots_offset = plutus_common.get_timerange_slots_offset(cluster_obj=cluster)
         timestamp_offset_ms = int(slots_offset * cluster.slot_length + 5) * 1_000
 
         # POSIX timestamp + offset
@@ -1117,10 +1118,7 @@ def test_ttl_horizon(
             *mint_txouts,
         ]
 
-        # Calculate 3k/f
-        offset_3kf = round(
-            3 * cluster.genesis["securityParam"] / cluster.genesis["activeSlotsCoeff"]
-        )
+        offset_3kf = clusterlib_utils.get_stability_window(cluster_obj=cluster)
 
         # Use 3k/f + `epoch_length` slots for ttl - this will not meet the `expect_pass` condition
         if ttl_offset == -1:
diff --git a/cardano_node_tests/utils/clusterlib_utils.py b/cardano_node_tests/utils/clusterlib_utils.py
index 5f5c40e5d..4a7a60795 100644
--- a/cardano_node_tests/utils/clusterlib_utils.py
+++ b/cardano_node_tests/utils/clusterlib_utils.py
@@ -1159,6 +1159,25 @@ def save_ledger_state(
     return json_file
 
 
+def get_stability_window(*, cluster_obj: clusterlib.ClusterLib) -> int:
+    """Return the stability window (`3k/f`) in slots.
+
+    Rounded down, so that the result is never above the window the ledger itself uses. A
+    caller that uses it as a limit therefore stays inside the window. The division is
+    exact on every testnet variant, so the rounding only guards against a variant that
+    picks a `securityParam` and `activeSlotsCoeff` that don't divide.
+
+    Args:
+        cluster_obj: An instance of `clusterlib.ClusterLib`.
+
+    Returns:
+        int: The number of slots in the stability window.
+    """
+    security_param = int(cluster_obj.genesis["securityParam"])
+    active_slots_coeff = float(cluster_obj.genesis["activeSlotsCoeff"])
+    return math.floor(3 * security_param / active_slots_coeff)
+
+
 def wait_for_epoch_interval(
     *,
     cluster_obj: clusterlib.ClusterLib,