The level densities and $gamma$-ray strength functions of $^{105,106,111,112}$Cd have been extracted from particle-$gamma$ coincidence data using the Oslo method. The level densities are in very good agreement with known levels at low excitation energy. The $gamma$-ray strength functions display no strong enhancement for low $gamma$ energies. However, more low-energy strength is apparent for $^{105,106}$Cd than for $^{111,112}$Cd. For $gamma$ energies above $approx$ 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.
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