Quantum-mechanical tunneling rates are determined, in the semiclassical approximation, by the action integral along a complex classical trajectory below the barrier. In asymmetric multidimensional potentials, the most efficient tunneling path can deviate markedly from the steepest-descent path down from the barrier. Normal-form theory allows to construct a coordinate transformation that brings the barrier into a symmetric shape and thus permits an easy identification of the tunneling path. I will illustrate this method by constructing tunneling paths for the hydrogen molecular ion in an electric field.