Eady's and Green's baroclinic instability problems are examined in N-level models with 2 ⩽ N ⩽ 180. As N is increased, both the maximum growth rate and the wavelength at which it occurs converge monotonically, without the irregular oscillatory behavior reported by Staley in a study of the instability of more complicated mean flows. Secondary and higher order maxima of growth rate occur amongst the short waves in the N-level Green problem, as noted by Arakawa and as found by Staley in the problems he studied. Each such spurious subsidiary maximum is associated with the occurrence of a critical level close to a model grid level. Regions of spurious stability may be associated with critical levels falling between model grid levels. A simple analytical model of these phenomena is proposed. It represents the potential vorticity gradient only at the grid level nearest to the critical level, and is quantitatively successful in reproducing the isolated subsidiary maxima found in the N-level Green problem.