Dynamical focusing of ensembles of neutral particles in energy and configuration space has been demonstrated recently (Petri et al. in Phys. Rev. E (R) 82:035204, 2010) using time-dependent elliptical billiards. The interplay of nonlinearity, dissipation, and driving yields the occurrence of attractors in the phase space of the billiard. Here, we show that dissipative oval billiards with slowly oscillating elliptical scatterers in the interior allow for a dynamical focusing on simple periodic trajectories with close to perfect efficiency. This setup should be more amenable to corresponding experiments of certain type which are briefly discussed.