For nonlinear sigma models in the unitary symmetry class, the nonlinear target space can be parameterized with cubic polynomials. This choice of coordinates has been known previously as the Dyson-Maleev parameterization for spin systems, and we show that it can be applied to a wide range of sigma models. The practical use of this parameterization includes simplification of diagrammatic calculations ( in perturbative methods) and of algebraic manipulations ( in non-perturbative approaches). We illustrate the use and specific issues of the Dyson-Maleev parameterization with three examples: the Keldysh sigma model for time-dependent random Hamiltonians, the supersymmetric sigma model for random matrices and the supersymmetric transfer-matrix technique for quasi-one-dimensional disordered wires. We demonstrate that nonlinear sigma models of unitary-like symmetry classes C and B/D also admit the Dyson-Maleev parameterization.