This paper presents efficient pruning algorithms for computing the DFT for a subset of output samples based on radix-2 decimation-in-time and decimation-in-frequency FFTs. They provide efficient implementations with a minimum number of stages. Comparisons are made with previously reported algorithms in terms of the computational complexity. The proposed algorithms are shown to provide a substantial reduction in the number of arithmetic operations, data transfers, address computations, and twiddle factor evaluations or accesses to the lookup table. The proposed algorithms retain all the features and characteristics, such as the simplicity and regularity, of the well-known Cooley-Tukey radix-2 FFT algorithms.