For generating PWM waveforms, it would be nice to have a state machine design that could expand to larger registers without increasing its depth. Synchronous ripple carry has O(N) depth, while lookahead carry has O(log N) depth, but designs with O(1) depth include ring counters, LFSRs, and Johnson counters. However, those three cases have disadvantages: ring counters require N bits to represent N states, while Johnson counters are almost as bad, requiring N/2. LFSRs are nearly optimal in flip-flop efficiency and can always work with depth of one or slightly more, but comparing LFSR states for beforeness is very difficult. In some cases it may be adequate to compare the LFSR state for equality.
Carry-save counters have depth of 1, but it is also not clear to me that they can be compared for greaterness with any reasonable degree of circuit depth. Also, they use twice as many bits as a regular binary counter, and while this isn’t as bad as a Johnson counter, it's significantly bad.
The context of all of this is that it would be nice to have counters that we can clock very quickly.