In the design of algorithms for the solution of stiff ordinary differential equation systems, high order Runge-Kutta methods seem to be attractive choices. However, it is now known that for many of these methods the order of accuracy that might be expected from the theoretical order is not realized in practical performance. The correct exponent for stiff problems, that is the B-convergence order, is often limited to the stage-order but in other cases is one higher than this. The present paper gives a criterion for distinguishing between these two possibilities for a particular model problem class and applies its conclusions to some special types of methods. These include singly implicit methods which seem to have quite good prospects for practical implementation.