Vibrationally resolved photoelectron spectra of SinH- (n=2-4) have been measured at a photodetachment wavelength of 355 nm (3.493 eV). The electron affinities of Si2H, Si3H, and Si4H are 2.31 +/- 0.01, 2.53 +/- 0.01, and 2.68 +/- 0.01 eV, respectively. Vibrational frequencies for the neutral ground states and a low-lying state of Si2H are also determined. Assignment of the electronic states and vibrational frequencies is facilitated by comparison with ab initio calculations. The calculations show that the H atom in Si4H and Si4H- is bonded to a single Si atom, in contrast to the bridged structures found for the smaller clusters. These calculations, along with photoelectron energy and angular distributions, yield a definitive assignment of the ground and nearly degenerate first excited states of Si2H.