A class of embedded, diagonally implicit Runge-Kutta formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is discussed. As well as being computationally efficient, these formulae have the additional facility, that an estimate of the local truncation error is available at every step and this estimate entails virtually no extra computational cost. The formulae derived are compared with various existing methods for a selection of stiff problems and are shown to be superior in certain cases.