Logging uncaught exceptions in Python

How do you cause uncaught exceptions to output via the logging module rather than to stderr?

I realize the best way to do this would be:

try:
    raise Exception, 'Throwing a boring exception'
except Exception, e:
    logging.exception(e)

But my situation is such that it would be really nice if logging.exception(...) were invoked automatically whenever an exception isn’t caught.