diff --git a/packages/geo/src/__tests__/bounds.test.ts b/packages/geo/src/__tests__/bounds.test.ts
index 04da86d5a..5ff53eabf 100644
--- a/packages/geo/src/__tests__/bounds.test.ts
+++ b/packages/geo/src/__tests__/bounds.test.ts
@@ -15,6 +15,9 @@ o.spec('Bounds', () => {
         o(new Bounds(1.1, 10.1, 12.2, 11.2).round().toJson()).deepEquals({ x: 1, y: 10, width: 12, height: 11 });
         o(new Bounds(1.4, 10.6, 12.2, 11.4).round().toJson()).deepEquals({ x: 1, y: 11, width: 13, height: 11 });
         o(new Bounds(0.4, 0.6, 2.4, 1.6).round().toJson()).deepEquals({ x: 0, y: 1, width: 3, height: 1 });
+
+        o(new Bounds(1.6, 10.6, 12.5, 11.5).round().toJson()).deepEquals({ x: 2, y: 11, width: 12, height: 11 });
+        o(new Bounds(1.6, 10.6, 12.5, 11.5).round(0.2).toJson()).deepEquals({ x: 1, y: 10, width: 13, height: 12 });
     });
 
     o('toBbox', () => {
diff --git a/packages/geo/src/bounds.ts b/packages/geo/src/bounds.ts
index b3f732cbc..2bd412ac2 100644
--- a/packages/geo/src/bounds.ts
+++ b/packages/geo/src/bounds.ts
@@ -158,11 +158,14 @@ export class Bounds implements BoundingBox {
 
     /**
      * Round dimensions to integers keeping the error a low as possible
+
+     * @param bias influence the rounding in favour of a larger area (+ve bias) or smaller area (-ve
+     * bias). Example: bias = 0.2 would round left and top down when < 0.7 and round right and bottom up when >= 0.3
      */
-    public round(): Bounds {
-        const x = Math.round(this.x);
-        const y = Math.round(this.y);
-        return new Bounds(x, y, Math.round(this.right) - x, Math.round(this.bottom) - y);
+    public round(bias = 0): Bounds {
+        const x = Math.round(this.x - bias);
+        const y = Math.round(this.y - bias);
+        return new Bounds(x, y, Math.round(this.right + bias) - x, Math.round(this.bottom + bias) - y);
     }
 
     public add(bounds: Point): Bounds {
diff --git a/packages/tiler/src/tiler.ts b/packages/tiler/src/tiler.ts
index f59c69c52..cef01906f 100644
--- a/packages/tiler/src/tiler.ts
+++ b/packages/tiler/src/tiler.ts
@@ -13,6 +13,9 @@ export interface RasterPixelBounds {
     tiff: Bounds;
 }
 
+/** The amount to bias the Bounds.round function to cover a larger, rather than smaller, area. */
+const ROUND_BIAS = 0.2;
+
 export class Tiler {
     /** Tile size for the tiler and sub objects */
     public readonly tms: TileMatrixSet;
@@ -78,7 +81,7 @@ export class Tiler {
     ): Composition | null {
         const source = Bounds.fromJson(img.getTileBounds(x, y));
 
-        const target = source.scale(scaleFactor, scaleFactor).add(raster.tiff).round();
+        const target = source.scale(scaleFactor, scaleFactor).add(raster.tiff).round(ROUND_BIAS);
 
         // Validate that the requested COG tile actually intersects with the output raster
         const tileIntersection = target.intersection(raster.tile);