Pruned fast Fourier transforms (FFTs) can be efficient alternatives to compute DFTs when the input vector is zero padded and/or several output elements are not required. In this correspondence, a new method to prune composite length FFTs is proposed. The proposed pruning method uses decimation in frequency (DIF) and decimation in time (DIT) to decompose a DFT into stages of smaller DFTs. The pruning process is carried out on the input stage and the output stage of the decomposed transform. The proposed pruning method is flexible since it can perform input and/or output pruning over any composite length FFT, action that no other pruning method reported in the literature can carry out. Additionally, no restriction exists with the number of consecutive inputs and consecutive outputs that can be used. Finally, it is shown that the proposed pruning method generates efficient pruned power-of-three and power-of-two length FFTs.