The presence of isomeric levels with half-lives in the microsecond range has been identified in 125,126,127,128 Cd. Neutron-rich Cd isotopes were produced from the fragmentation of a 120 MeV/nucleon 136 Xe beam and uniquely identified through their time-of-flight, energy loss, and total kinetic energy. γ rays from these isomeric levels were measured with an array of Ge detectors that were gated for 15 µs by a particle implantation trigger from a stack of Si detectors. The γ rays observed in the decay of 126,128 Cd isomers populate low-energy levels previously identified in the β decay of 126,128 Ag. The γ rays found in the decay of 125,127 Cd isomers are consistent with expected yrast structures observed in lighter, odd-mass Cd isotopes. The appearance of these isomers at the point where N/Z exceeds 1.6 is interpreted as an indication of the onset of a weakened neutron-neutron interaction that has been proposed for 134 Sn, whose N/Z also exceeds 1.6.