The use of time-domain boundary integral equations has proved very ef fective and effcient for three dimensional acoustic and electromagnetic wave equations. In even dimensions and when some dissipation is present, time-domain boundary equations contain an infinite memory tail. Due to this, computation for longer times becomes exceedingly expensive. In this talk we show how fast and oblivious convolution quadrature, initially designed for parabolic problems, can be used to signicantly reduce both the cost and the memory requirements of computing this tail. We analyse Runge-Kutta based algorithms and show the result of some numerical experiments.