The 737 is pretty similar to the 747 apparently, we have a full thrust rating setting (26k on our 800s, 24k/22k on the 700s) and two fixed derates at 24 and 22k on the 800, 22k/20k and 20k/18k on the 700s, there are three climb thrust settings as well (CLIMB, CLIMB1 and CLIMB2). Usually climb thrust is selected automatically based on fixed derate and assumed temperature (in short based on take off N1) and is user selectable to any other climb thrust setting. Climb 1 usually washes out by around 10.000ft and Climb 2 around 15.000ft.
In my outfit they changed the SOP to always select full climb thrust whenever an unrestricted climb is likely. Wouldn't make sense in the london TMA for example or around paris or moskow, but pretty much elsewhere it does. That way we nearly always have a pretty big increase in climb thrust at the thrust reduction altitude. By the way, full climb thrust in an unrestricted climb saves around 40 to 50kgs of fuel per take off. Doesn't sound much, but in a large fleet it makes a lot of money at the end of the year, and it is one of very few fuel saving measures that is actually fun.