Got a new toy to play with. It's a commercial tilt-shift lens called a Lensbaby Composer. This particular model has been discontinued in the U.S., being replaced by the much more expensive Composer Pro.
I'm quite happy with the plain old Composer, thank you. I think it's more than adequate for my needs and ability. It comes with an assortment of apertures that you drop into place on top of the lens. They are held in place magnetically. The wider the aperture, the more pronounced the blur.
You shoot this thing in aperture priority mode, and the camera more or less sets the speed to 1/60 sec. Here's a sample shot at f 2.8, using the built-in flash.