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The "no-hair" theorem states that astrophysical black holes are fullycharacterised by just two numbers: their mass and spin. The gravitational-waveemission from a perturbed black-hole consists of a superposition of dampedsinusoids, known as \textit{quasi-normal modes}. Quasi-normal modes arespecified by three integers $(\ell,m,n)$: the $(\ell, m)$ integers describe theangular properties and $(n)$ specifies the (over)tone. If the no-hair theoremholds, the frequencies and damping times of quasi-normal modes are determineduniquely by the mass and spin of the black hole, while phases and amplitudesdepend on the particular perturbation. Current tests of the no-hair theorem,attempt to identify these modes in a semi-agnostic way, without imposing priorson the source of the perturbation. This is usually known as \textit{black-holespectroscopy}. Applying this framework to GW150914, the measurement of thefirst overtone led to the confirmation of the theorem to $20\%$ level. We show,however, that such semi-agnostic tests cannot provide strong evidence in favourof the no-hair theorem, even for extremely loud signals, given the increasingnumber of overtones (and free parameters) needed to fit the data. This can besolved by imposing prior assumptions on the origin of the perturbed black holethat can further constrain the explored parameters: in particular, ourknowledge that the ringdown is sourced by a binary black hole merger. Applyingthis strategy to GW150914 we find a natural log Bayes factor of $\sim 6.5$ infavour of the Kerr nature of its remnant, indicating that the hairy objecthypothesis is disfavoured with $<1:600$ with respect to the Kerr black-holeone.

Black-hole spectroscopy, the no-hair theorem and GW150914: Kerr vs. Occam