Multi-band speech recognition is powerful in band-limited noise, when the recognizer of the noisy band, which is less reliable, can be given less weight in the recombination process. An accurate decision on which bands can be considered as reliable and which bands are less reliable due to corruption by noise is usually hard to take. In this article, we investigate a maximum-likelihood (ML) approach to adapting the combination weights of a multi-band system. The Gaussian Mixture Model parameters are kept constant, while the combination weights are iteratively updated to maximize the data likelihood. Unsupervised offline and online weights adaptation are compared to use of equal weights, and `cheating' weights where the noisy band is known, as well as to the fullband system. Initial tests show that both ML-weighting strategies show a robustness gain on band-limited noise.