Alpha-decay properties of the isotope ¹⁹¹At were investigated for the first time and the decay properties of ¹⁹³At and ¹⁹⁵At were studied with improved accuracy. The nuclei were produced in fusion-evaporation reactions of ⁵⁴Fe and ⁵⁶Fe ions with ¹⁴¹Pr and ¹⁴²Nd targets. The fusion products were separated in-flight using the gas-filled recoil separator RITU and implanted into a position-sensitive silicon detector. The isotopes were identified using position, time and energy correlations between the implants and subsequent alpha decays. New information concerning the low-lying states in the corresponding alpha-decay daughter nuclei ¹⁸⁷Bi, ¹⁸⁹Bi and ¹⁹¹Bi was also gained using alpha-gamma coincidences. ; This work was supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2002-2005 (Project No. 44875, Nuclear and Condensed Matter Physics Programme at JYFL).