diff --git a/src/cdk/overlay/position/connected-position-strategy.spec.ts b/src/cdk/overlay/position/connected-position-strategy.spec.ts
index 0ba80be29cd5..6195ea0ca8b6 100644
--- a/src/cdk/overlay/position/connected-position-strategy.spec.ts
+++ b/src/cdk/overlay/position/connected-position-strategy.spec.ts
@@ -326,6 +326,28 @@ describe('ConnectedPositionStrategy', () => {
         expect(Math.floor(overlayRect.left)).toBe(Math.floor(originRect.left));
       });
 
+      it('should allow for the fallback positions to specify their own offsets', () => {
+        originElement.style.bottom = '0';
+        originRect = originElement.getBoundingClientRect();
+        strategy = positionBuilder
+          .connectedTo(
+            fakeElementRef,
+            {originX: 'start', originY: 'top'},
+            {overlayX: 'start', overlayY: 'top'})
+          .withFallbackPosition(
+            {originX: 'start', originY: 'top'},
+            {overlayX: 'start', overlayY: 'bottom'},
+            -100, -100);
+
+        strategy.withOffsetY(50).withOffsetY(50);
+        strategy.attach(fakeOverlayRef(overlayElement));
+        strategy.apply();
+
+        let overlayRect = overlayElement.getBoundingClientRect();
+        expect(Math.floor(overlayRect.bottom)).toBe(Math.floor(originRect.top - 100));
+        expect(Math.floor(overlayRect.left)).toBe(Math.floor(originRect.left - 100));
+      });
+
     });
 
     it('should emit onPositionChange event when position changes', () => {
diff --git a/src/cdk/overlay/position/connected-position-strategy.ts b/src/cdk/overlay/position/connected-position-strategy.ts
index 3c26d310823b..a9a946524fd6 100644
--- a/src/cdk/overlay/position/connected-position-strategy.ts
+++ b/src/cdk/overlay/position/connected-position-strategy.ts
@@ -192,8 +192,12 @@ export class ConnectedPositionStrategy implements PositionStrategy {
    */
   withFallbackPosition(
       originPos: OriginConnectionPosition,
-      overlayPos: OverlayConnectionPosition): this {
-    this._preferredPositions.push(new ConnectionPositionPair(originPos, overlayPos));
+      overlayPos: OverlayConnectionPosition,
+      offsetX?: number,
+      offsetY?: number): this {
+
+    const position = new ConnectionPositionPair(originPos, overlayPos, offsetX, offsetY);
+    this._preferredPositions.push(position);
     return this;
   }
 
@@ -296,9 +300,13 @@ export class ConnectedPositionStrategy implements PositionStrategy {
       overlayStartY = pos.overlayY == 'top' ? 0 : -overlayRect.height;
     }
 
+    // The (x, y) offsets of the overlay based on the current position.
+    let offsetX = typeof pos.offsetX === 'undefined' ? this._offsetX : pos.offsetX;
+    let offsetY = typeof pos.offsetY === 'undefined' ? this._offsetY : pos.offsetY;
+
     // The (x, y) coordinates of the overlay.
-    let x = originPoint.x + overlayStartX + this._offsetX;
-    let y = originPoint.y + overlayStartY + this._offsetY;
+    let x = originPoint.x + overlayStartX + offsetX;
+    let y = originPoint.y + overlayStartY + offsetY;
 
     // How much the overlay would overflow at this position, on each side.
     let leftOverflow = 0 - x;
diff --git a/src/cdk/overlay/position/connected-position.ts b/src/cdk/overlay/position/connected-position.ts
index 66cc66ce680e..ff9114fd8538 100644
--- a/src/cdk/overlay/position/connected-position.ts
+++ b/src/cdk/overlay/position/connected-position.ts
@@ -33,7 +33,12 @@ export class ConnectionPositionPair {
   overlayX: HorizontalConnectionPos;
   overlayY: VerticalConnectionPos;
 
-  constructor(origin: OriginConnectionPosition, overlay: OverlayConnectionPosition) {
+  constructor(
+    origin: OriginConnectionPosition,
+    overlay: OverlayConnectionPosition,
+    public offsetX?: number,
+    public offsetY?: number) {
+
     this.originX = origin.originX;
     this.originY = origin.originY;
     this.overlayX = overlay.overlayX;
diff --git a/src/lib/menu/menu-trigger.ts b/src/lib/menu/menu-trigger.ts
index f135a8e63798..abc1a1a11998 100644
--- a/src/lib/menu/menu-trigger.ts
+++ b/src/lib/menu/menu-trigger.ts
@@ -354,9 +354,6 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
       // to the edges of the trigger, instead of overlapping it.
       overlayFallbackX = originX = this.menu.xPosition === 'before' ? 'start' : 'end';
       originFallbackX = overlayX = originX === 'end' ? 'start' : 'end';
-
-      // TODO(crisbeto): this should be a function, once the overlay supports it.
-      // Right now it will be wrong for the fallback positions.
       offsetY = overlayY === 'bottom' ? MENU_PANEL_TOP_PADDING : -MENU_PANEL_TOP_PADDING;
     } else if (!this.menu.overlapTrigger) {
       originY = overlayY === 'top' ? 'bottom' : 'top';
@@ -372,10 +369,12 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
             {overlayX: overlayFallbackX, overlayY})
         .withFallbackPosition(
             {originX, originY: originFallbackY},
-            {overlayX, overlayY: overlayFallbackY})
+            {overlayX, overlayY: overlayFallbackY},
+            undefined, -offsetY)
         .withFallbackPosition(
             {originX: originFallbackX, originY: originFallbackY},
-            {overlayX: overlayFallbackX, overlayY: overlayFallbackY});
+            {overlayX: overlayFallbackX, overlayY: overlayFallbackY},
+            undefined, -offsetY);
   }
 
   /** Cleans up the active subscriptions. */