diff --git a/OpenRA.Game/Traits/Player/Shroud.cs b/OpenRA.Game/Traits/Player/Shroud.cs
index 9a7b2e6bd3..b494e75927 100644
--- a/OpenRA.Game/Traits/Player/Shroud.cs
+++ b/OpenRA.Game/Traits/Player/Shroud.cs
@@ -186,20 +186,22 @@ namespace OpenRA.Traits
 				Hash += 1;
 		}
 
-		public static IEnumerable<PPos> ProjectedCellsInRange(Map map, WPos pos, WDist range, int maxHeightDelta = -1)
+		public static IEnumerable<PPos> ProjectedCellsInRange(Map map, WPos pos, WDist minRange, WDist maxRange, int maxHeightDelta = -1)
 		{
 			// Account for potential extra half-cell from odd-height terrain
-			var r = (range.Length + 1023 + 512) / 1024;
-			var limit = range.LengthSquared;
+			var r = (maxRange.Length + 1023 + 512) / 1024;
+			var minLimit = minRange.LengthSquared;
+			var maxLimit = maxRange.LengthSquared;
 
 			// Project actor position into the shroud plane
 			var projectedPos = pos - new WVec(0, pos.Z, pos.Z);
 			var projectedCell = map.CellContaining(projectedPos);
 			var projectedHeight = pos.Z / 512;
 
-			foreach (var c in map.FindTilesInCircle(projectedCell, r, true))
+			foreach (var c in map.FindTilesInAnnulus(projectedCell, minRange.Length / 1024, r, true))
 			{
-				if ((map.CenterOfCell(c) - projectedPos).HorizontalLengthSquared <= limit)
+				var dist = (map.CenterOfCell(c) - projectedPos).HorizontalLengthSquared;
+				if (dist <= maxLimit && (dist == 0 || dist > minLimit))
 				{
 					var puv = (PPos)c.ToMPos(map);
 					if (maxHeightDelta < 0 || map.ProjectedHeight(puv) < projectedHeight + maxHeightDelta)
@@ -210,7 +212,7 @@ namespace OpenRA.Traits
 
 		public static IEnumerable<PPos> ProjectedCellsInRange(Map map, CPos cell, WDist range, int maxHeightDelta = -1)
 		{
-			return ProjectedCellsInRange(map, map.CenterOfCell(cell), range, maxHeightDelta);
+			return ProjectedCellsInRange(map, map.CenterOfCell(cell), WDist.Zero, range, maxHeightDelta);
 		}
 
 		public void AddSource(object key, SourceType type, PPos[] projectedCells)
diff --git a/OpenRA.Mods.Common/Effects/RevealShroudEffect.cs b/OpenRA.Mods.Common/Effects/RevealShroudEffect.cs
index dba6cdf389..8de19d75c2 100644
--- a/OpenRA.Mods.Common/Effects/RevealShroudEffect.cs
+++ b/OpenRA.Mods.Common/Effects/RevealShroudEffect.cs
@@ -52,7 +52,7 @@ namespace OpenRA.Mods.Common.Effects
 			if (range == WDist.Zero)
 				return NoCells;
 
-			return Shroud.ProjectedCellsInRange(map, pos, range)
+			return Shroud.ProjectedCellsInRange(map, pos, WDist.Zero, range)
 				.ToArray();
 		}
 
diff --git a/OpenRA.Mods.Common/Traits/AffectsShroud.cs b/OpenRA.Mods.Common/Traits/AffectsShroud.cs
index 6eb87e0c07..d7cc0c90e7 100644
--- a/OpenRA.Mods.Common/Traits/AffectsShroud.cs
+++ b/OpenRA.Mods.Common/Traits/AffectsShroud.cs
@@ -17,6 +17,8 @@ namespace OpenRA.Mods.Common.Traits
 {
 	public abstract class AffectsShroudInfo : ConditionalTraitInfo
 	{
+		public readonly WDist MinRange = WDist.Zero;
+
 		public readonly WDist Range = WDist.Zero;
 
 		[Desc("If >= 0, prevent cells that are this much higher than the actor from being revealed.")]
@@ -61,15 +63,16 @@ namespace OpenRA.Mods.Common.Traits
 		PPos[] ProjectedCells(Actor self)
 		{
 			var map = self.World.Map;
-			var range = Range;
-			if (range == WDist.Zero)
+			var minRange = Info.MinRange;
+			var maxRange = Range;
+			if (maxRange <= minRange)
 				return NoCells;
 
 			if (Info.Type == VisibilityType.Footprint)
 			{
 				// PERF: Reuse collection to avoid allocations.
 				footprint.UnionWith(self.OccupiesSpace.OccupiedCells()
-					.SelectMany(kv => Shroud.ProjectedCellsInRange(map, kv.First, range, Info.MaxHeightDelta)));
+					.SelectMany(kv => Shroud.ProjectedCellsInRange(map, map.CenterOfCell(kv.First), minRange, maxRange, Info.MaxHeightDelta)));
 				var cells = footprint.ToArray();
 				footprint.Clear();
 				return cells;
@@ -79,7 +82,7 @@ namespace OpenRA.Mods.Common.Traits
 			if (Info.Type == VisibilityType.GroundPosition)
 				pos -= new WVec(WDist.Zero, WDist.Zero, self.World.Map.DistanceAboveTerrain(pos));
 
-			return Shroud.ProjectedCellsInRange(map, pos, range, Info.MaxHeightDelta)
+			return Shroud.ProjectedCellsInRange(map, pos, minRange, maxRange, Info.MaxHeightDelta)
 				.ToArray();
 		}