The photodetachment cross sections for H- and Li- in the vicinity of the If(n=2-4) and Li(n=3-4) thresholds are calculated. A discrete numerical basis set, combined with the method of complex rotation, isr used to construct highly correlated descriptions of both initial and final states. The energies and widths of the doubly excited states are calculated directly and compared with results from experiments and other calculations when available: Other resonance parameters for photoexcitation from the ground slate to the autodetaching states, describing the shape and the strength of the resonances, are-also calculated. Mass polarization was considered for the doubly excited States of H-, but was found to be much smaller than the present experimental accuracy. The possibility of describing a photodetachment resonance with a Fano profile, i.e., with a few resonance parameters connected to properties of a specific autodetaching state, is investigated and it is concluded that most resonances in Li- in the region studied, where overlapping resonances are common, cannot be meaningfully analyzed in this way.