The split-radix algorithm for the discrete Fourier transform of length-2^m is by now fairly popular. First, we give the reason why the split-radix algorithm is better tant any single-radix algorithm on length 2^m DFT's. Then, the split-radix approach is generalized to length-p^m DFT's. It is shown that whenever a radix-p^2 outperforms a radix-p / p^2 algorithm will outperform both of them. As an exemple, a radix-3/9 algorithm is developed for length 3^m DFT's.