VERIFIED SOLUTION i
There is a table of buffers that overlap and it is desired to remove the overlap and make the buffers adjacent to each other.
1. Make the buffer table editable.
2. Select both overlapping buffers (hold the shift key to select multiple geographies).
3. Choose Objects>Set Target.
4. Make the cosmetic layer editable.
5. Turn on snap mode (hit "S" key on keyboard).
6. Using the drawing tools, draw a polygon that starts outside the buffers, goes through the area of intersection, and then continues around one of the buffers.
In Snap mode, the cursor will turn to a large cross when over a node. Use this feature to make sure the polygon goes through the area of intersection at the node closest to the point where the outer edge of each buffer intersect.
(Version 7.x and later allow splitting with a polyline, so just draw a polyline that bisects the area of overlap or "football")
7. Make the buffer table editable.
8. Choose Objects>Split (or Polyline Split if using version 7.0 and a polyline was created in Step 6). Aggregate the data accordingly.
9. Make the cosmetic layer editable and delete the polygon (or polyline) created in step 6.
10. Make the buffer table editable and delete each half of the "football" (area of overlap).
(Note that one half of the "football" could be underneath one of the buffers - use ctrl-click to select this piece)
This is the result:
UPDATED: March 30, 2017