The β-decay of odd-A, neutron-rich Ti57 and V59 are studied. More precise β-decay half-lives of 98±5 and 97±2 ms are deduced for Ti57 and V59, respectively. In addition, β-delayed γ-ray spectroscopy is used to deduce β-decay branching ratios and establish the low-energy-level structures of the daughter nuclides. The new data for levels in V57 and Cr59 are compared with the results of shell-model calculations completed in the full pf model space. Both V57 and Cr59 show evidence of modest oblate deformation near the ground state.