  One of the most interesting sources of gravitational waves (GWs) for LISA is
the inspiral of compact objects on to a massive black hole (MBH), commonly
referred to as an "extreme-mass ratio inspiral" (EMRI). The small object,
typically a stellar black hole (bh), emits significant amounts of GW along each
orbit in the detector bandwidth. The slowly, adiabatic inspiral of these
sources will allow us to map space-time around MBHs in detail, as well as to
test our current conception of gravitation in the strong regime. The event rate
of this kind of source has been addressed many times in the literature and the
numbers reported fluctuate by orders of magnitude. On the other hand, recent
observations of the Galactic center revealed a dearth of giant stars inside the
inner parsec relative to the numbers theoretically expected for a fully relaxed
stellar cusp. The possibility of unrelaxed nuclei (or, equivalently, with no or
only a very shallow cusp) adds substantial uncertainty to the estimates. Having
this timely question in mind, we run a significant number of direct-summation
$N-$body simulations with up to half a million particles to calibrate a much
faster orbit-averaged Fokker-Planck code. We then investigate the regime of
strong mass segregation (SMS) for models with two different stellar mass
components. We show that, under quite generic initial conditions, the time
required for the growth of a relaxed, mass segregated stellar cusp is shorter
than a Hubble time for MBHs with $M_\bullet \lesssim 5 \times 10^6 M_\odot$
(i.e. nuclei in the range of LISA). SMS has a significant impact boosting the
EMRI rates by a factor of $\sim 10$ for our fiducial models of Milky Way type
galactic nuclei.
