For a homogeneous system divisible into identical, weakly interacting subsystems, the multicanonical procedure can be accelerated if it is first applied to determine the density of states for a single subsystem. This result is then employed to approximate the state density of a subsystem with twice the size that forms the starting point of a new multicanonical iteration. Since this compound subsystem interacts less on average with its environment, iterating this sequence of steps rapidly generates the state density of the full system.