The paper is concerned with an extension of the classical relation between the
flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively
stable flames). At low Lewis numbers the corresponding flame-flow system suffers
short-wavelength instability, making the associated initial value problem ill-posed. In this study
the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with
a reduced model based on a coupled system of second-order dynamic equations for the flame
interface and its temperature. As an illustration the new model is applied for description of
diffusively unstable stagnation-point flow flames.