The level densities and γ-ray strength functions of 105,106,111,112 Cd have been extracted from particle-γ coincidence data using the Oslo method. The level densities are in very good agreement with known levels at low excitation energy. The γ-ray strength functions display no strong enhancement for low γ energies. However, more low-energy strength is apparent for 105,106 Cd than for 111,112 Cd. For γ energies above ≈ 4 MeV, there is evidence for some extra strength, similar to what has been previously observed for the Sn isotopes. The origin of this extra strength is unclear; it might be due to E1 and M1 transitions originating from neutron skin oscillations or the spin-flip resonance, respectively.