In this short paper we consider the effect of the presence of conducting sidewalls of finite thickness on the onset of convection in a two-dimensional porous cavity. Two cases are considered where the outer boundaries of the sidewalls are either perfectly insulating or perfectly conducting. A unified theory is presented which combines both these cases, and the stability properties of the overall system is found to undergo a full transition from that of the classical Darcy-Benard problem to that of the degenerate system studied in detail by Rees and Tyvand (J Eng Math 49: 181-193, 2004).