A method of speaker adaptation for continuous density mixture Gaussian HMMs is presented. A transformation for the component mixture means is derived by linear regression using a maximum likelihood optimisation criteria. The best use is made of the available adaptation data by dening equivalence classes of regression transforms and tying one regression matrix to a number of component mixtures. This allows successful adaptation on any amount of adaptation data. Tests on the RM1 database show that successful adaptation can be achieved with only 11 seconds of speech, and performance converges towards that of speaker dependent training as more adaptation data is used.