Abstract <p>Reduced models for combustion often are based on low-dimensional manifolds (LDMs) in state space, to which the evolution of the system is restricted. To describe the evolution of states on the manifold, an explicit parametrization of the manifold, which allows expressing the thermochemical states on the manifold by known functions of some parameter, can be useful. For technical reasons, a&#xa0;parametrization of a low-dimensional manifold in terms of a linear combination of species (and possibly other state variables, e.g., temperature) is desired. This linear combination is often chosen such that it allows physical interpretation in terms of a chemical progress, and is therefore termed progress variable (PV). A widespread task in the development and application of reduced combustion models is therefore to find a progress variable-based parametrization for a given low-dimensional manifold. This paper describes a lightweight, effective method for constructing (if at all possible) such a linear combination-based progress variable. Compared to other, existing methods for progress variable construction, the method is simple to implement, does not requires nonlinear optimization procedures and is therefore computationally highly efficient and robust. Application of the method to a wide range of combustion systems (ignition, flame extinction, featuring multicomponent fuels) shows its good performance and robustness.</p>