The half-lives of isomeric states of fully ionized ¹⁴⁴Tb, ¹⁴⁹Dy and ¹⁵¹Er have been measured. These nuclides were produced via fragmentation of about 900 MeV/u ²⁰⁹Bi projectiles, separated in flight with the fragment separator (FRS) and stored in the cooler ring (ESR). The decay times of the cooled fragments have been measured with time-resolved Schottky spectrometry. We observed for the first time drastic increases of the half-lives of bare isomers by factors of up to 30 compared to their neutral counterparts. This is due to the exclusion of the strong internal conversion and electron-capture channels in the radioactive decay of these bare nuclei. The experimental results are in good agreement with theoretical calculations.