Each year almost a million fish are aged from otoliths, primarily to estimate proportions at age for use in stock assessments. The preparation and reading of otoliths is time-consuming and thus expensive. Two techniques have been proposed to reduce costs. The first is length-mediated estimation, in which the length distribution from a large sample of fish is converted to an age distribution, using information (usually in the form of an age–length key) from a smaller sample containing length and age data. The second is to infer age from otolith weight (and/or other otolith measurements). These two cost-saving ideas are combined in a new method, length-mediated mixture analysis. It requires three samples – one with lengths only, one with lengths and otolith measurements, and one with lengths, otolith measurements and ages – and estimation is by maximum likelihood. The use of this method, which can be thought of as a generalisation of three established methods of age inference, is illustrated in two simulation experiments in a cost-benefit framework.