We study a recently proposed compound two degrees of freedom planar leg mechanism consisting of a four-bar linkage and a pantograph. In this mechanism, one degree of freedom is used for normal walking to provide an ovoid path which emulates that of humans while the other is used only when necessary to walk over obstacles. Potential advantages of such a compound mechanism are fast locomotion, minimal energy loss, simplicity in controller design, and slenderness of the leg. To exploit these to the fullest, a multiobjective optimization-based design problem formulation is proposed with the following four design objectives: (i) minimum leg height, (ii) minimum of the maximum joint forces, (iii) minimum leg mass, and (iv) minimum energy loss for a walking cycle. In addition, this problem formulation takes into account a combination of mechanism requirements and structural requirements. Several tradeoff solutions are obtained using the Consol-Optcad interactive optimization-based design package.