diff --git a/OpenRA.Game/Map/Map.cs b/OpenRA.Game/Map/Map.cs
index c733e3d90e..acbcedc433 100644
--- a/OpenRA.Game/Map/Map.cs
+++ b/OpenRA.Game/Map/Map.cs
@@ -870,7 +870,7 @@ namespace OpenRA
 		// it rounds the actual distance up to the next integer so that this call
 		// will return any cells that intersect with the requested range circle.
 		// The returned positions are sorted by distance from the center.
-		public IEnumerable<CPos> FindTilesInAnnulus(CPos center, int minRange, int maxRange)
+		public IEnumerable<CPos> FindTilesInAnnulus(CPos center, int minRange, int maxRange, bool allowOutsideBounds = false)
 		{
 			if (maxRange < minRange)
 				throw new ArgumentOutOfRangeException("maxRange", "Maximum range is less than the minimum range.");
@@ -878,20 +878,24 @@ namespace OpenRA
 			if (maxRange > TilesByDistance.Length)
 				throw new ArgumentOutOfRangeException("maxRange", "The requested range ({0}) exceeds the maximum allowed ({1})".F(maxRange, MaxTilesInCircleRange));
 
+			Func<CPos, bool> valid = Contains;
+			if (allowOutsideBounds)
+				valid = MapTiles.Value.Contains;
+
 			for (var i = minRange; i <= maxRange; i++)
 			{
 				foreach (var offset in TilesByDistance[i])
 				{
 					var t = offset + center;
-					if (Contains(t))
+					if (valid(t))
 						yield return t;
 				}
 			}
 		}
 
-		public IEnumerable<CPos> FindTilesInCircle(CPos center, int maxRange)
+		public IEnumerable<CPos> FindTilesInCircle(CPos center, int maxRange, bool allowOutsideBounds = false)
 		{
-			return FindTilesInAnnulus(center, 0, maxRange);
+			return FindTilesInAnnulus(center, 0, maxRange, allowOutsideBounds);
 		}
 	}
 }
diff --git a/OpenRA.Game/Traits/World/Shroud.cs b/OpenRA.Game/Traits/World/Shroud.cs
index 3c718ec491..452bea039f 100644
--- a/OpenRA.Game/Traits/World/Shroud.cs
+++ b/OpenRA.Game/Traits/World/Shroud.cs
@@ -112,7 +112,7 @@ namespace OpenRA.Traits
 			var limit = radius.RangeSquared;
 			var pos = map.CenterOfCell(position);
 
-			foreach (var cell in map.FindTilesInCircle(position, r))
+			foreach (var cell in map.FindTilesInCircle(position, r, true))
 				if ((map.CenterOfCell(cell) - pos).HorizontalLengthSquared <= limit)
 					yield return cell;
 		}
@@ -129,6 +129,11 @@ namespace OpenRA.Traits
 			foreach (var c in visible)
 			{
 				var uv = c.ToMPos(map);
+
+				// Force cells outside the visible bounds invisible
+				if (!map.Contains(uv))
+					continue;
+
 				visibleCount[uv]++;
 				explored[uv] = true;
 			}
@@ -147,7 +152,11 @@ namespace OpenRA.Traits
 				return;
 
 			foreach (var c in visible)
-				visibleCount[c.ToMPos(map)]--;
+			{
+				// Cells outside the visible bounds don't increment visibleCount
+				if (map.Contains(c))
+					visibleCount[c.ToMPos(map)]--;
+			}
 
 			visibility.Remove(a);
 			Invalidate(visible);