  How well is the vacuum Kerr geometry a good description of the dark, compact
objects in our universe? Precision measurements of accreting matter in the deep
infrared and gravitational-wave measurements of coalescing objects are finally
providing answers to this question. Here, we study the possibility of resonant
excitation of the modes of the central object -- taken to be very compact but
horizonless -- during an extreme-mass-ratio inspiral. We show that for very
compact objects resonances are indeed excited. However, the impact of such
excitation on the phase of the gravitational-wave signal is negligible, since
resonances are crossed very quickly during inspiral.
