We present Regge-model predictions for the p(gamma,K+)Sigma0 and n(gamma,K+)Sigma- differential cross sections and photon-beam asymmetries in the resonance region. The reaction amplitude encompasses the exchange of K+(494) and K*+(892) Regge-trajectories, introducing a mere three free parameters. These are fitted to the available p(gamma,K+)Sigma0 data beyond the resonance region. The n(gamma,K+)Sigma- amplitude is obtained from the p(gamma,K+)Sigma0 one through SU(2) isospin symmetry considerations.