minimizing overlap in random rectangles

Question

I have a number of possibly overlapping rectangles, of random size and position within a fixed plane. Since these rectangles are random, some may not overlap:

|-----
|    |    |----|
|----|    |    |
          |----|

Some may overlap by just one corner:

|-----|
|  |--|--|
|--|--|  |
   |-----|

Some may be contained inside another rectangle:

|----------------|
|                |
|   |-----|      |
|   |     |      |
|   |-----|      |
|----------------|

Some may pass through another rectangle:

   |----------------|
   |                |
|--|-------------------|
|  |                |  |
|--|-------------------|
   |----------------|

etc.

I'm trying to find an algorithm that gives me a set of rectangles that represent the same area as the input set, but without overlapping. Some cases are obvious - rectangles contained within a larger rectangle can be discarded, and rectangles that overlap on a corner can be split into three rectangles, as can rectangles that pass through another rectangle. What I'm looking for, is a generic algorithm that deals with all these cases. I don't care much if it's not brilliantly efficient - the input set is rather small (25 rectangles at most)

Finding rectangles that overlap is easy, but it quickly gets harder from there, especially when you consider that one rectangle may overlap with multiple other rectangles.

This is doing my head in. Any suggestions?

Update:

I just realised one more thing:

I can either run this algorithm at the time that the rectangles are added tot he set, one by one, or after all the rectangles have been added. It may be easier to do it as the rectangles are being added, since you only have one rectangle to consider, but you still need to account for the situation where a single rectangle overlaps multiple other rectangles.