We measured the strange-meson spectrum in the scattering reaction $K^- + p\to K^-\pi^-\pi^+ + p$ with the COMPASS spectrometer at CERN. Using the world's largest sample of this reaction, we performed a comprehensive partial-wave analysis of the mesonic final state. It substantially extends the strange-meson spectrum covering twelve states with masses up to $2.4\, \text{GeV}/c^2$. We observe the first candidate for a crypto-exotic strange meson with $J^P=0^-$ and find $K_3$ and $K_4$ states consistent with predictions for the ground states.

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