Can't build cube because of broken aggregations

I just removed some dimensions from a cube I had built, to clean things up a bit. When I tried to build the cube it failed because of references to the now-missing-dimensions in the aggregations. So I went to Design Aggregations to rebuild them. This failed because of the now-missing-dimensions.
Here's my workaround:
I re-added the now-missing-dimensions, then rebuilt the cube to test it. It succeeded, so I went back to the Design Aggregations tool, and started it. I then stopped it as soon as it had built 1 aggregation. I then removed the dimensions I wanted to remove and rebuilt the aggregations.