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

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... 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.