  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.
