I'm using arcGIS 10.1 on an i5 win7 machine with 16g RAM. Not a xeon but have never had big problems even with large datasets.
Here's what I'm doing: I have point data representing locations within specified political boundaries. They represent the centroids of districts contained within larger geographic units which are 1) not uniform in size or 2) shape.
My goal is to create a buffer around these points, but to do so such that the larger boundaries act as the minimum bounding geography. So the radius of the buffer would not exceed the closest point of the border of the larger geography. This would give me buffers which were totally contained in the larger geography and would vary with the size of the larger bounding geography. I've looked at min. bounding geography features, and this seems to do something different--i.e. it would create a larger buffer around the larger geography.
To answerers: The issue with this is that it will give me an irregular shape--what I'm really trying to get here is to preserve the circle shape, but to make sure that it doesn't exceed any point of the larger bounding geography. Clipping would give me 'pac man' kind of shapes that are not ideal. As to more than 1 step--Oh of course! I'd take a dozen steps if I can get to the solution. And welcome more cumbersome but technically simple approaches.