A variation on this theme is the ground-adjustable propeller. As its name implies, a qualified technician with the correct tools can change the blades' angle of attack on the ground, allowing per-flight optimization for cruise or climb, but not both.
To qualify as an LSA the airplane (we'll skip copters, gliders and such) must have fixed landing gear and a fixed-pitch or ground-adjustable propeller, no more than two seats and a maximum takeoff weight of 1320 pounds.