The collinear ion-beam depletion technique is used to measure absolute photofragmentation cross sections of small silver-cluster ions in the range from 2.3 to 5.7 eV. Giant resonances are found which can be interpreted in terms of a collective electron oscillation. The optical spectra of spherical Ag9+ and Ag21+ show a large blue-shift of the resonance energy relative to the respective experimental surface value. For non-spherical clusters, a splitting of the giant resonance is found, in qualitative accordance with jellium calculations.