The decays of the πd3/2 ground states of 156Ta and 160Re have been studied in detail using the GREAT spectrometer. More than 7000 160Re nuclei were produced in reactions of 290- and 300-MeV 58Ni ions with an isotopically enriched 106Cd target and separated in flight using the RITU separator. The proton and α decays of the πd3/2 level were confirmed and the half-life and branching ratios of this state were determined with improved precision to be t1/2=611±7 μs and bp=89±1% and bα=11±1%, respectively. The α-decay branch populated the ground state of 156Ta, allowing improved values for the proton-decay energy and half-life to be obtained (Ep=1011±5 keV; t1/2=106±4 ms). The β decay of this level was identified for the first time and a branching ratio of bβ=29±3% was deduced. The spectroscopic factors deduced from these measurements are compared with predictions.