  The computation of the self-force constitutes one of the main challenges for
the construction of precise theoretical waveform templates in order to detect
and analyze extreme-mass-ratio inspirals with the future space-based
gravitational-wave observatory LISA. Since the number of templates required is
quite high, it is important to develop fast algorithms both for the computation
of the self-force and the production of waveforms. In this article we show how
to tune a recent time-domain technique for the computation of the self-force,
what we call the Particle without Particle scheme, in order to make it very
precise and at the same time very efficient. We also extend this technique in
order to allow for highly eccentric orbits.
