The dynamics of two‐dimensional Rayleigh–Be´nard convection rolls are studied in a finite layer with no‐slip, fixed temperature upper and lower boundaries and no‐slip insulating side walls. The dominant mechanism controlling the number of rolls seen in the layer is an instability concentrated near the side walls. This mechanism significantly narrows the band of stable wavenumbers although it can take a time comparable to the long (horizontal) diffusion time scale to operate.