The use of reliable or at least realistic friction models is a key factor in simulation studies related to antilock brake control systems. In the literature a plethora of strongly nonlinear tyre-road friction models are available. Certain models have singular expressions in the arguments of exponential terms in the vicinity of zero car body velocity though this region has practical significance. Since the parameters of these singular models may quickly vary in time with the variation of the road conditions their realtime identification was evaded in a paper that applied a simple observer instead. This method has been improved in the present paper by applying a novel adaptive technique for compensating the effects of the imprecisely known other (i.e. not related to the tyre-road friction) parameters. By the use of a particular friction model it was found via simulations that the adaptive technique can considerably shorten the braking distance.