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The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetryreductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the JimboMiwa (JM) equation, we find that three well-known (2+1)-dimensional models-the asymmetric Nizhnik-NovikovVeselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation-can all be obtained as the conditional similarity reductions of the JM equation.