Theoretical analysis of ordered power-of-two fast Fourier transforms (PO2FFTs) demonstrates that the most efficient algorithms for hypercube architectures may not always use nearest-neighbor communication. It is shown that an ordered PO2FFT can be obtained with just d interprocessor communications for any r if the restriction that all communications are distance one is removed. The two interprocessor communications requirements of this algorithm are determined. Packets of size N/2d+1 are transmitted in both of the ordered PO2FFT algorithms. The time complexity of both the distance one and the distance two algorithms is discussed.