We present a class of suboptimal multiple-symbol differential detectors (MSDDs) for differential unitary space-time (ST) codes in a time-selective Rayleigh flat-fading channel. These noncoherent detectors, termed Fano ST-MSDDs, employ the well-known Fano algorithm as their decoding engines. Their bit-error rate (BER) performance is excellent, as there is no irreducible error floor, even at very high fade rates. Compared with the sphere decoder, which is optimal, our best detector, termed an on-demand bi-Fano ST-MSDD, suffers only a 0.3 dB degradation in power efficiency. However, its computational complexity, as a function of the signal-to-noise ratio (SNR), is consistently lower than that of the sphere decoder and does not experience the exponential growth in complexity in the latter when the SNR decreases. It can thus be concluded that the Fano algorithm is a powerful detection strategy for differential ST codes in fading channels. Our main contribution is in making the modifications and improvements to the Fano algorithm that enables this realization. The innovations include the bi-Fano, edge-bi-Fano, and on-demand bi-Fano search strategies, as well as a new dynamic threshold adjustment scheme for avoiding unnecessary back-and-forth node evaluations during backtracking