What's the best way to clean a salad spinner? We had taco salads last night for dinner.  Cleaning the little bits of shredded lettuce out of the salad spinner seemed to take forever.  Despite scrubbing and lots of rinsing, little bits of lettuce were still clinging to the inner bowl (in between the slits in the bowl).  I finally resorted to picking out the lettuce bits by hand in order to be sure I got them all.  Is there an easy way to clean this thing?

We could try washing the lettuce first, then shredding, but what about the pre-packaged lettuce that's already shredded?  I'd heard you're still supposed to wash that too.
I've never done this, but what about filling the bowl with water, lowering the spinning basket into it so the lettuce shreds lift off, then dumping it out?