Threshold behavior in inner-shell photodetachment is studied for the first time, specifically with 2-, 3-, or 4-electron emission from He- and S-. The threshold shapes are surprisingly consistent with the Wigner threshold law in all cases, despite large PCI effects observed in He-. In S-, the s-wave law is observed to agree with the data over an unprecedented range, more than an order of magnitude greater than predictions, and allows for the observation of the d-wave component. The measurements also demonstrate a means for obtaining precise core-excitation energies of free atoms.