We explore space-time boundary element methods (BEM) for transient wave problems with prescribed Dirichlet data and zero initial conditions. Our approach is based on the formulations introduced in [3], where the associated boundary integral equations exhibit continuity and satisfy inf-sup conditions in trace spaces of matching regularity. Existing literature on BEM for transient wave problems has predominantly concentrated on first-kind for- mulations and their discretisations. In contrast, this talk focuses on the discretisation of the double layer boundary integral operator for the wave equation. We present the first BEM discretisations of second- kind operators for the wave equation for which stability is guaranteed and a complete numerical analysis is offered. Furthermore, we extend our study to higher-dimensional problems, offering numerical results that, to the best of our knowledge, have not been reported previously.