Using Intersect Tool on a layer with overlapping polygons

[Anonymous User]

Original User: jrv27

I'm performing an intersect between two polygon layers: a 1mile radius polygon (Layer1) and the US Census Block Groups. Many polygons in Layer1 are very close together and overlap quite a bit, so the output layer has many slivers of the same census block group in Layer1. Is there a way to keep the intersect output from splitting the intersected Block Group between the overlapping polygons?  I tried ranking Layer1 as 1, but it didn't seem to have any effect. I've attached two images to help illustrate my issue.  Thanks for any insight you might have! (I'm using ArcGIS10 at the ArcEditor level)

The red outline is the radius polygon, with the census block groups in a grey outline:
[ATTACH=CONFIG]15403[/ATTACH]

Zoomed in to show the overlap areas more clearly:
[ATTACH=CONFIG]15404[/ATTACH]

[Anonymous User]

Original User: mdenil

Either dissolve the Layer1 polygons before the intersect,
or perform the overlay with one polygon from Layer1 at a time,
or dissolve the Census layer after the Intersect using approriate attributes to re-attach the splinters.

... Depends on what you want out of the intersect.