Removing sliver polygons in ArcGIS Desktop?

I unioned 2 layers into 1 layer, and it created sliver polygons.

I used the elimination tool to merge them with neighboring polygons.

As as result, it merges all sliver polygons to only one polygon (selected in the picture).

What I need, is that, every sliver polygon to be added to its neighboring polygon.

How that could be achieved?

I am using ArcGIS Desktop 10.

Answer

I solved it myself.

After unioning the layers, the silver polygons were added as a single polygon.

Therefore I had to use the Explode Multi-part Feature tool from advanced editing toolbar, which separated the polygon into multiple single polygons.

Then the Elimination tool was able to add the polygons to neighboring polygons easily.