Families of p^k-ary sequences with small Hamming crosscorrelation are required for hopping patterns in asynchronous frequency-hopping spread-spectrum multiple-access communication systems. Lower bounds on the out-of-phase auto correlation and on the crosscorrelation of sequences of given length and alphabet size are derived in [l]，and a method of constructing families of sequences that uniformly realize these bounds is presented as well. In this paper，a commonest method of constructing families of frequency-hopping sequences with optimal Hamming correlation properties is presented，taking the method in [1] as its special case. By driving the frequency synthesizer from k inconsecutive stages Tather than from k consecutive stages，we can partially solve the Hop-and-Stay problem existing in [1].