The optical emissions in a large number of bright sprites observed over one storm in 1998 exhibit a relaxation that is closely exponential in time. This feature was unexpected but might be explained by the presence of quasi-constant electric fields over times of several milliseconds, in which case the optical relaxation would be a direct indication of the exponentially changing electron density. The relaxation rates for sprites appear to have an upper bound that is consistent with the dissociative electron attachment rates expected at sprite altitudes. The experimental results are consistent with existing large-scale electrodynamic models of sprites as well as with the streamer mechanism as the underlying physical process for sprite ionization.