Fast-timing measurements were performed recently in the region of the medium-mass 103,105,107 Cd isotopes, produced in fusion evaporation reactions. Emitted γ-rays were detected by eight HPGe and five LaBr3:Ce detectors working in coincidence. Results on new and re-evaluated half-lives are discussed within a systematic of transition rates. The 7/2 + 1 states in 103,105,107 Cd are interpreted as arising from a single-particle excitation. The half-life analysis of the 11/2 − 1 states in 103,105,107 Cd shows no change in the single-particle transition strength as a function of the neutron number.