diff --git a/app/broadcast_areas/__init__.py b/app/broadcast_areas/__init__.py
index c9e40ec89..338763fe3 100644
--- a/app/broadcast_areas/__init__.py
+++ b/app/broadcast_areas/__init__.py
@@ -80,9 +80,8 @@ class BroadcastArea(SortableMixin):
 
     @property
     def estimated_bleed_in_m(self):
-        if self.id.endswith(CITY_OF_LONDON.WARDS):
-            return 500
-        return 5_900 - (math.log(self.phone_density, 10) * 1_250)
+        estimated_bleed = 5_900 - (math.log(self.phone_density, 10) * 1_250)
+        return max(500, min(estimated_bleed, 5000))
 
     @property
     def estimated_bleed_in_degrees(self):
diff --git a/tests/app/broadcast_areas/test_broadcast_area.py b/tests/app/broadcast_areas/test_broadcast_area.py
index 7c904ce55..705916cb5 100644
--- a/tests/app/broadcast_areas/test_broadcast_area.py
+++ b/tests/app/broadcast_areas/test_broadcast_area.py
@@ -315,7 +315,7 @@ def test_phone_density(
 @pytest.mark.parametrize('area, expected_bleed_in_m, expected_bleed_in_degrees', (
     (
         # Islington (most dense in UK)
-        'lad20-E09000019', 488, 0.00439
+        'lad20-E09000019', 500, 0.00449
     ),
     (
         # Cordwainer Ward (City of London)
@@ -332,7 +332,7 @@ def test_phone_density(
     ),
     (
         # Highland (least dense in UK)
-        'lad20-S12000017', 5_095, 0.0458
+        'lad20-S12000017', 5_000, 0.0449
     ),
 ))
 def test_estimated_bleed(
diff --git a/tests/app/main/views/test_broadcast.py b/tests/app/main/views/test_broadcast.py
index ba473e376..2fa9a5140 100644
--- a/tests/app/main/views/test_broadcast.py
+++ b/tests/app/main/views/test_broadcast.py
@@ -649,7 +649,7 @@ def test_broadcast_page(
         'Islington remove',
     ], [
         'An area of 9.7 square miles Will get the alert',
-        'An extra area of 4.6 square miles is Likely to get the alert',
+        'An extra area of 4.7 square miles is Likely to get the alert',
         '200,000 to 300,000 phones',
     ]),
 ))