The anisotropic plastic behaviour of metals (without prestrain) can be described rather accurately by means of polycrystalline deformation models based on the Taylor theory. This crystallographic anisotropy can be incorporated into finite-element simulations by means of a semi-analytical approach, using plastic potentials of which the coefficients are derived from the Taylor model and the texture. The convexity of the adopted expressions has since long been a problematic issue. In this paper a new class of potential functions in strain-rate space is introduced. These have the advantage that convexity can be strictly imposed. The new formulation is critically assessed for a bcc material with a sharp model texture consisting of a Gaussian distribution centered around the (100) orientation and with a spread of 11 degrees.