As a recent variant of the classical viscous tuned mass damper (VTMD), the pounding tuned mass damper (PTMD) relies on impact with the main structure as the source of energy dissipation. Unlike the symmetrical double-sided PTMD, the asymmetrical single-sided PTMD appears especially prom-ising because of its limited sensitivity to the excitation amplitude. However, a thorough assessment of its performance is still lacking, particularly under seismic loading. In this paper, a single-sided PTMD having zero impact gap in the undeformed state is investigated under the assumption of a stereo-mechanical non-smooth impact model. First, its mathematical model is derived and proved to be nonlinear but homogeneous, which ensures an amplitude-independent effectiveness on linear structures. In this light, an Hinf- and an H2-optimum design strategies are then proposed for a PTMD on a single-degree-of-freedom linear structure, whereby the optimal PTMD is determined by mini-mizing, respectively, the Hinf and the H2 norm of the input-output transfer function from the ground acceleration to the structural displacement, approximated by numerical simulations under repeated sinusoidal and white noise excitations. The obtained Hinf- and H2-optimum PTMDs are finally com-pared with the corresponding Hinf- and H2-optimum VTMDs, considering various mass ratios and several input types (including a large set of natural seismic records), and admitting possible unde-sired changes of the structural frequency. The results show that the PTMD is generally less effective than the VTMD if the structure responds as nominally expected, but sensibly more effective in the event of structural variations. They also show that the Hinf design is less effective than the H2 design in nominal conditions, but more robust against uncertainties. In conclusion, the zero-gap PTMD proves a promising alternative to traditional TMD types, and this study offers simple and effective solutions for its optimal seismic design.