We report a systematic study on the conditions under which an endothermic phase transition can enforce layered convection. Two-dimensional numerical calculations of convection in a domain containing a divariant phase change were performed in the framework of the ''extended Boussinesq approximation,'' i.e., considering the effects of adiabatic gradient, latent heat, and frictional heating in the energy equation. We find that the critical value of the negative Clapeyron slope, which must be surpassed in order to induce layered convection, decreases in magnitude with increasing Rayleigh number Ra in the range 104≤Ra≤2¿106. Near the critical Clapeyron slope, vacillations between double- and single-layer convection or strongly leaking double-layer convection are possible. The breakdown into layers is influenced very little by the latent heat release but depends solely on the phase boundary deflection caused by lateral temperature differences. The value of the critical Clapeyron slope also seems little affected by the width of the transition zone or by its depth. A possible superplastic rheology within the transition zone would tend to favor layered convection. Scaling the model results to the 670-km discontinuity of the earth's mantle as a possible endothermic phase boundary, we estimate the critical Clapeyron slope to be in the range of -4 to -8 MPa/K (-40 to -80 bar/K). The possiblity that the spinel→perovskite+periclase transition is within this range appears to be remote but certainly cannot be neglected.