An extension of the so-called QUEST method of Watson and Pelli (1979, 1983) is proposed. In contrast to the traditional QUEST method, the new method, the MUEST method, offers the possibility of simultaneously estimating more than one parameter of a parametric representation of the psychometric function. Knowledge about more parameters gives a higher guarantee of obtaining correct threshold values. The basic extension itself is analytically quite modest and can be explained in a few sentences. However, the involved additional techniques, like the placing of stimulus levels, require a more extensive description, which is presented here. Copyright 1997 Academic Press. Copyright 1997 Academic Press