We present a new measurement of the branching ratio of the decay K-L-->pi (
+/-) e(-/+) nu (e)gamma (K-e3 gamma) with respect to K-L-->pi (-/+) e(-/+)
nu (e) (K(e)3), and the first study of the photon energy spectrum in this d
ecay. We find BR (K-e3 gamma,E-gamma* > 30 MeV, theta (e gamma)* > 20 degre
es)/BR (K-e3) = 0.908+/-0.008(stat)(-0.012)(+0.013)(syst)%. Our measurement
of the spectrum is consistent with inner bremsstrahlung as the only source
of photons in K-e3 gamma.