The multi-band processing paradigm for noise robust ASR was originally motivated by the observation that human recognition appears to be based on independent processing of separate frequency sub-bands, and also by ``missing data'' results which have shown that ASR can be made significantly more robust to band-limited noise if noisy sub-bands can be detected and then ignored. Of the different multi-band models which have been proposed, only the ``Full Combination'' or ``all-wise'' multi-band HMM/ANN hybrid approach allows us to consistently overcome the difficult problem of deciding which sub-bands are noisy, by integrating over all possible positions of noisy sub-bands. While this system has performed better than any other multi-band system which we have tested, %[in the framework of both HMM/MLP hybrid systems and standard HMMs], we have also found that it only shows significantly improved robustness to noise when the noise is strongly band-limited. In real noise environments this is rarely the case. An alternative paradigm for noise robust ASR is multi-stream, as opposed to multi-band, ASR. In multi-stream processing the aim is to combine evidence from a number of different representations of the full speech signal, rather than from a number of frequency sub-bands. Several models for multi-stream ASR have recently reported significant performance improvements for speech with real noise. In this article we first present evidence to show how multi-band ASR has a strong advantage over the baseline system with band-limited noise, but no clear advantage with wide-band noise. We then show how the principled theoretical basis for Full Combination multi-band ASR can be directly transfered to multi-stream combination, and we show how this model can be used to combine data streams comprising three commonly used types of acoustic features. Preliminary results show significantly improved recognition with clean speech.