Borrowing the structure of building blocks from potential hydrodynamics, we set up model evolution equations to mimic moderately wrinkled three-dimensional flames expanding in gaseous premixtures. These evolution equations incorporate a hydrodynamic instability, local curvature effects, a Huygens-type nonlinearity, and can cope with broad-banded forcing whenever needed. Pseudo-spectral integrations in the Legendre–Fourier basis yield evolutions of the whole front that are in striking qualitative agreement with experiments on free or weakly forced propagations. Our results are robust against educated changes in the modelling. Provided an accurate evolution equation is available, this approach can simulate expanding flames which are quite a bit larger than what DNS can currently handle, at least in the chosen configurations.