This paper presents an adaptive procedure applied to measurements of speech intelligibility using the modified rhyme test. It is argued that the required speech-to-noise (SNR) ratio could be estimated with sufficient accuracy with as few as 25 utterances. The present procedure is based on the maximum a posteriori criterion, and it is demonstrated how the standard deviation of the SNR estimate can be improved by about 0.5 dB compared to a previously published method based on the maximum likelihood procedure.