diff --git a/domain/epc/property_overlays/main_heating_system_overlay.py b/domain/epc/property_overlays/main_heating_system_overlay.py
index ded78999..e763fea7 100644
--- a/domain/epc/property_overlays/main_heating_system_overlay.py
+++ b/domain/epc/property_overlays/main_heating_system_overlay.py
@@ -164,5 +164,10 @@ def main_heating_overlay_for(
             sap_main_heating_code=code,
             meter_type=_meter_for(code),
             main_heating_control=_control_for(code),
+            # A landlord override describes the existing dwelling, so its assumed
+            # off-peak meter must not downgrade a more-off-peak cert meter
+            # (e.g. a 24-hour all-low tariff). Measures, which re-meter for real,
+            # build their HeatingOverlay directly and leave this False.
+            keep_existing_off_peak_meter=True,
         )
     )
diff --git a/domain/modelling/scoring/overlay_applicator.py b/domain/modelling/scoring/overlay_applicator.py
index 93875bbf..36fedb83 100644
--- a/domain/modelling/scoring/overlay_applicator.py
+++ b/domain/modelling/scoring/overlay_applicator.py
@@ -152,6 +152,22 @@ _SAP_HEATING_FIELDS: tuple[str, ...] = (
 _ENERGY_SOURCE_FIELDS: tuple[str, ...] = ("meter_type", "mains_gas")
 
 
+def _is_off_peak_meter(meter_type: object) -> bool:
+    """True iff the meter resolves to an off-peak Table 12a tariff (not the
+    STANDARD single-rate column). Unparseable / absent meters count as not
+    off-peak so a coherent override meter still applies to them."""
+    from domain.sap10_calculator.exceptions import UnmappedSapCode
+    from domain.sap10_calculator.tables.table_12a import (
+        Tariff,
+        tariff_from_meter_type,
+    )
+
+    try:
+        return tariff_from_meter_type(meter_type) is not Tariff.STANDARD
+    except UnmappedSapCode:
+        return False
+
+
 def _fold_heating(epc: EpcPropertyData, overlay: HeatingOverlay) -> None:
     """Write a `HeatingOverlay`'s non-``None`` fields onto the (copied) dwelling,
     routing each to its home: the primary ``main_heating_details[0]``, the
@@ -181,8 +197,25 @@ def _fold_heating(epc: EpcPropertyData, overlay: HeatingOverlay) -> None:
         epc.has_hot_water_cylinder = overlay.has_hot_water_cylinder
     for field_name in _ENERGY_SOURCE_FIELDS:
         value = getattr(overlay, field_name)
-        if value is not None:
-            setattr(epc.sap_energy_source, field_name, value)
+        if value is None:
+            continue
+        # A landlord heating override's assumed meter (Dual for off-peak
+        # systems) is a coherent default, not a re-metering of the cert: when it
+        # opts in (`keep_existing_off_peak_meter`), don't downgrade a cert that
+        # already lodges a MORE off-peak meter (e.g. a 24-hour all-low tariff) to
+        # the overlay's 7-hour E7 — keep the cert's (more specific) one. Single/
+        # unknown existing meters still receive the off-peak meter, and a switch
+        # to single-rate still resets it (its desired value isn't off-peak).
+        # Heating MEASURES leave the flag False — they re-meter for real
+        # (Elmhurst re-lodges 18-hour → Dual on a storage install).
+        if (
+            field_name == "meter_type"
+            and overlay.keep_existing_off_peak_meter
+            and _is_off_peak_meter(value)
+            and _is_off_peak_meter(epc.sap_energy_source.meter_type)
+        ):
+            continue
+        setattr(epc.sap_energy_source, field_name, value)
 
 
 # `SolarOverlay` fields all live on `sap_energy_source` (the home of the SAP
diff --git a/domain/modelling/simulation.py b/domain/modelling/simulation.py
index 457fa094..401aaf27 100644
--- a/domain/modelling/simulation.py
+++ b/domain/modelling/simulation.py
@@ -193,6 +193,13 @@ class HeatingOverlay:
     # sap_energy_source
     meter_type: Optional[str] = None
     mains_gas: Optional[bool] = None
+    # A landlord heating-system override DESCRIBES the existing dwelling, so its
+    # assumed off-peak (`meter_type`) is a coherent default, not a re-metering:
+    # it must not downgrade a cert that already lodges a MORE off-peak meter
+    # (e.g. a 24-hour all-low tariff → the overlay's 7-hour E7). A heating
+    # MEASURE re-meters for real (Elmhurst re-lodges 18-hour → Dual on a storage
+    # install), so it leaves this False. `_fold_heating` reads it.
+    keep_existing_off_peak_meter: bool = False
 
 
 @dataclass(frozen=True)