  Gravitational waveforms and fluxes from extreme mass--ratio inspirals can be
computed using time--domain methods with accuracy that is fast approaching that
of frequency--domain methods. We study in detail the computational efficiency
of these methods for equatorial orbits of fast spinning Kerr black holes, and
find the number of modes needed in either method --as functions of the orbital
parameters-- in order to achieve a desired accuracy level. We then estimate the
total computation time and argue that for high eccentricity orbits the
time--domain approach is more efficient computationally. We suggest that in
practice low--$m$ modes are computed using the frequency--domain approach, and
high--$m$ modes are computed using the time--domain approach, where $m$ is the
azimuthal mode number.
