Currently, my bash terminal/tab title is set based on the directory I'm in. For example:

bob@bobscomputer:~/i/had/some/great/pie/yesterday

This isn't very useful if I have multiple tabs open side-by-side. For example, if I have 4 tabs of the above dir open side-by-side, all I see is

bob@bobscomputer:~/i/had...

4 times.

I'd like all my terminal titles to be set automatically to just the last part of the path. In the example above, I'd like the title to be

yesterday

Obviously, the title should change when I change directories. I'd like to do this without changing my prompt, so the prompt and the terminal title should be different.

Is there a way to do this?