Incomplete-fusion reactions have been used to study high-spin states in 171Tm. Gamma rays and conversion electrons were measured using pulsed-beam conditions for enhanced isomer sensitivity. A Kπ=19/2+, three-quasiparticle isomer was identified, with a half-life of 1.7(2) µs. The faster than expected transition rates from the isomer can be understood as being due to a chance near-degeneracy, with mixing between the isomeric state and the Iπ=19/2+ member of the one-quasiparticle rotational bands to which it decays. The implied mixing matrix element is 12(2) eV.