A non-linear least-squares (NLS) method is used without regularization to recover the release history of a groundwater contaminant plume from its current measured spatial distribution. The flow system is assumed to be one-dimensional, with the plume originating from a known single site. The solution is found to be very sensitive to noise and to the extent to which the plume is dissipated. Although the NLS method is extremely sensitive to measurement errors for the gradual release scenario, it can resolve the release histories for catastrophic release scenarios reasonably well, even in the presence of moderate measurement errors. A number of synthetic numerical examples are analysed. We find that for catastrophic contaminant releases the NLS method may be an alternative to the Tikhonov regularization approach.