The diffusional-thermal instability of diffusion flames is studied in a constant-density two-dimensional counterflow diffusion flame, to investigate an instability mechanism by which periodic wrinkling of the reaction sheet can occur. Attention is focused on flames with small departures of the Lewis number from unity and with small values of the stoichiometric mixture fraction, so that the premixed-flame regime can be employed for activation-energy asymptotics. Results of the analysis show that roll patterns, in which the reaction sheet is wrinkled in the direction parallel to the dominant strain, will occur when (1) the Lewis number of the more completely consumed reactant is less than a critical value (approximate to 0.7) and (2) the flame is subject to a strain late close to that at the quasisteady extinction. Parametric results for the instability onset conditions, obtained through numerical solutions, reveal that flames with smaller values of the Lewis number and stoichiometric mixture fraction and with larger values of the Zel＇dovich number tend to be more unstable.