A study is made of the relative stability of disparate horizontal wavelengths of two-dimensional, nonlinear, thermal convection between poorly conducting boundaries. Although the narrower horizontal scales grow most rapidly and tend to dominate the cell pattern initially, an asymptotic theory suggests that the cell-size would eventually evolve to one much broader than the layer depth. This prediction of the asymptotic theory is tested against fully nonlinear spectral and finite-difference models. In some selected numerical experiments, the nonlinear models are consistent with the weakly nonlinear theory only in slightly supercritical conditions. At a Rayleigh number above twice critical, the evolution to broad scales does not occur. The cell-size is locked into the narrower cell-size that first grew and stabilized. The results are applied to mesoscale cellular convection in the atmosphere.