We discuss the acceptance and sensitivity of a small air-shower imaging system to detect earth-skimming ultrahigh-energy tau neutrinos. The instrument we study is located on top of a mountain and has an azimuthal field of view of $360^circ$. We find that the acceptance and sensitivity of such a system is close to maximal if it is located about 2 km above ground, has a vertical field of view of $5^circ$, allows the reconstruction of an at least $0.3^circ$ long air-shower image, and features an effective light-collection area of $10$ m$^2$ in any direction. After three years of operation, an imaging system with these features achieves an all-flavor neutrino flux sensitivity of $5times10^{-9}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$ at $2times10^8$ GeV.
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