The paper deals with the problem of improving the performance of the adaptive transform coder which operates on noisy speech. We propose to estimate the short-time spectral amplitude (STSA) of the original speech and to utilise the noisy phase prior to the encoding process. The appropriate minimum mean-square error STSA estimator is derived and the system is examined in encoding speech which has been degraded by uncorrelated additive wideband spectrally flat noise. The above approach improves the quality of the encoded speech in the sense that the output noise level and the irregularities characteristic to the directly encoded noisy speech are reduced. However, the encoded speech loses some of its crispness.