Lifetimes of states in the ground-state bands of (70)Se and (72)Se were measured using the recoil-distance Doppler shift method. The results deviate significantly from earlier measurements, requiring a revision of the conclusions drawn from a recent Coulomb excitation experiment concerning the shape of (70)Se. The new results lead to a coherent picture of shape coexistence in the neutron-deficient selenium and krypton isotopes. The coexistence and evolution of oblate and prolate shapes in this mass region is for the first time consistently described by new Hartree-Fock-Bogolyubov-based configuration-mixing calculations which were performed using the Gogny D1S interaction.