In the paper, we present the results of our study using a recursive discrete Hartley transform technique to compute discrete Fourier transforms. We also introduce an improved in-place and in-order prime-factor mapping to effectively realise composite-length DFTs. In using these new techniques, the speed of computation is comparable to that of the Winograd Fourier transform algorithm (WFTA), whereas the program size of the present approach is much smaller than that of the WFTA. This approach is most suitable for the cases where there are restrictions on program lengths.