The 143Dy nucleus has been studied with the 92Mo (54Fe, 2pn γ) reaction at 240 MeV incident energy. A rich variety of structures was observed at high spin. The nearly spherical vh 11/2 I=11/2 isomer is the basis of a negative parity irregular yrast structure which is observed up to I=51/2. A positive parity band presenting a large dynamic moment of inertia was observed, similar to the deformation enhanced vi 13/2 bands known to exist in this mass region. However, we propose an alternative assignment for this band, namely the triaxial collective minimum with β=0.2 predicted by total Routhian surface calculations for a N osc = 4 quasineutron excitation coupled to pairs of aligned quasiparticles. Another negative parity structure, with strong M1 and weak E2 crossover transitions, was observed.