High-spin states in 171Re have been studied using the reaction Sb-123(Cr-52,4n)171Re. A back-bend in the i13/2 band of a Re nucleus has been fully delineated for the first time. A new back-bend has also been observed in the 5/2+[402] band and other bands have been extended to higher spin and added to the level scheme. Band crossings are interpreted using the CSM and three-band mixing calculations. These appear to show evidence for shape coexistence and configuration-dependent neutron pairing.