diff --git a/core/src/main/kotlin/fr/sncf/osrd/standalone_sim/StandaloneSimulation.kt b/core/src/main/kotlin/fr/sncf/osrd/standalone_sim/StandaloneSimulation.kt
index 5a3466289e6..5dc6877878a 100644
--- a/core/src/main/kotlin/fr/sncf/osrd/standalone_sim/StandaloneSimulation.kt
+++ b/core/src/main/kotlin/fr/sncf/osrd/standalone_sim/StandaloneSimulation.kt
@@ -191,7 +191,9 @@ fun makeMRSPResponse(speedLimits: Envelope): MRSPResponse {
 
 /**
  * Build the final envelope from the max effort / provisional envelopes. The final envelope modifies
- * the margin ranges to match the scheduled points.
+ * the margin ranges to match the scheduled points. The added time is distributed over the different
+ * margin ranges, following a logic described in details on the OSRD website:
+ * https://osrd.fr/en/docs/reference/design-docs/timetable/#combining-margins-and-schedule
  */
 fun buildFinalEnvelope(
     maxEffortEnvelope: Envelope,
@@ -204,6 +206,9 @@ fun buildFinalEnvelope(
     fun getEnvelopeTimeAt(offset: Offset<TravelledPath>): Double {
         return provisionalEnvelope.interpolateDepartureFromClamp(offset.distance.meters)
     }
+    fun getMaxEffortEnvelopeTimeAt(offset: Offset<TravelledPath>): Double {
+        return maxEffortEnvelope.interpolateDepartureFromClamp(offset.distance.meters)
+    }
     var prevFixedPointOffset = Offset<TravelledPath>(0.meters)
     var prevFixedPointDepartureTime = 0.0
     val marginRanges = mutableListOf<AllowanceRange>()
@@ -217,24 +222,51 @@ fun buildFinalEnvelope(
         val sectionTime =
             getEnvelopeTimeAt(point.pathOffset) - getEnvelopeTimeAt(prevFixedPointOffset)
         val arrivalTime = prevFixedPointDepartureTime + sectionTime
-        var extraTime = point.arrival.seconds - arrivalTime
-        if (extraTime < 0.0) {
-            // TODO: raise a warning
-            standaloneSimLogger.warn("impossible scheduled point")
-            extraTime = 0.0
-        }
-        marginRanges.addAll(
-            distributeAllowance(
-                maxEffortEnvelope,
-                provisionalEnvelope,
-                extraTime,
-                margins,
-                prevFixedPointOffset,
-                point.pathOffset
+        val extraTime = point.arrival.seconds - arrivalTime
+        if (extraTime >= 0.0) {
+            marginRanges.addAll(
+                distributeAllowance(
+                    maxEffortEnvelope,
+                    provisionalEnvelope,
+                    extraTime,
+                    margins,
+                    prevFixedPointOffset,
+                    point.pathOffset
+                )
             )
-        )
+            prevFixedPointDepartureTime = arrivalTime + extraTime + (point.stopFor?.seconds ?: 0.0)
+        } else {
+            // We need to *remove* time compared to the provisional envelope.
+            // Ideally we would distribute the (negative) extra time following the same logic as
+            // when it's positive. But this is tricky: as we get closer to max effort envelope (hard
+            // limit), we need to redistribute the time in some cases.
+            // We currently handle this by ignoring the distribution over different margin ranges,
+            // we just set the time for the scheduled point without more details. It will be easier
+            // to handle it properly when we'll have migrated to standalone sim v3.
+            val maxEffortSectionTime =
+                getMaxEffortEnvelopeTimeAt(point.pathOffset) -
+                    getMaxEffortEnvelopeTimeAt(prevFixedPointOffset)
+            val earliestPossibleArrival = prevFixedPointDepartureTime + maxEffortSectionTime
+            var maxEffortExtraTime = point.arrival.seconds - earliestPossibleArrival
+            if (maxEffortExtraTime < 0.0) {
+                standaloneSimLogger.warn("impossible scheduled point")
+                // TODO: raise warning: scheduled point isn't possible
+                maxEffortExtraTime = 0.0
+            } else {
+                standaloneSimLogger.warn("scheduled point doesn't follow standard allowance")
+                // TODO: raise warning: scheduled point doesn't follow standard allowance
+            }
+            marginRanges.add(
+                AllowanceRange(
+                    prevFixedPointOffset.distance.meters,
+                    point.pathOffset.distance.meters,
+                    FixedTime(maxEffortExtraTime)
+                )
+            )
+            prevFixedPointDepartureTime =
+                earliestPossibleArrival + maxEffortExtraTime + (point.stopFor?.seconds ?: 0.0)
+        }
         prevFixedPointOffset = point.pathOffset
-        prevFixedPointDepartureTime = arrivalTime + extraTime + (point.stopFor?.seconds ?: 0.0)
     }
     val pathEnd = Offset<TravelledPath>(maxEffortEnvelope.endPos.meters)
     if (prevFixedPointOffset < pathEnd) {
diff --git a/tests/tests/test_timetable_v2.py b/tests/tests/test_timetable_v2.py
index 6409e875dc5..0025e14252e 100644
--- a/tests/tests/test_timetable_v2.py
+++ b/tests/tests/test_timetable_v2.py
@@ -93,3 +93,52 @@ def test_conflicts(
     assert response.status_code == 200
     actual_conflicts = {conflict["conflict_type"] for conflict in response.json()}
     assert actual_conflicts == expected_conflict_types
+
+
+def test_scheduled_points_with_incompatible_margins(
+    small_infra: Infra,
+    timetable_v2: TimetableV2,
+    fast_rolling_stock: int,
+):
+    requests.post(f"{EDITOAST_URL}infra/{small_infra.id}/load").raise_for_status()
+    train_schedule_payload = [
+        {
+            "comfort": "STANDARD",
+            "constraint_distribution": "STANDARD",
+            "initial_speed": 0,
+            "labels": [],
+            "options": {"use_electrical_profiles": False},
+            "path": [
+                {"id": "start", "track": "TC0", "offset": 185000},
+                {"id": "end", "track": "TD0", "offset": 24820000},
+            ],
+            "power_restrictions": [],
+            "rolling_stock_name": "fast_rolling_stock",
+            "schedule": [
+                {
+                    "at": "start",
+                },
+                {
+                    "at": "end",
+                    "arrival": "PT4000S",
+                },
+            ],
+            "margins": {"boundaries": [], "values": ["100%"]},
+            "speed_limit_tag": "MA100",
+            "start_time": "2024-05-22T08:00:00.000Z",
+            "train_name": "name",
+        }
+    ]
+    response = requests.post(
+        f"{EDITOAST_URL}/v2/timetable/{timetable_v2.id}/train_schedule", json=train_schedule_payload
+    )
+    response.raise_for_status()
+    train_id = response.json()[0]["id"]
+    response = requests.get(f"{EDITOAST_URL}/v2/train_schedule/{train_id}/simulation/?infra_id={small_infra.id}")
+    response.raise_for_status()
+    content = response.json()
+    sim_output = content["final_output"]
+    travel_time_seconds = sim_output["times"][-1] / 1_000
+
+    # Should arrive roughly 4000s after departure, even if that doesn't fit the margins
+    assert abs(travel_time_seconds - 4_000) < 2