Exclusive data on the reactions pp -> ppK+K- and pp -> pK+ Lambda/Sigma0 have been taken at the cooler synchrotron COSY close to threshold. At equal excess energies, an enhancement of the Lambda/Sigma0 ratio by one order of magnitude has been observed compared to data at higher excess energies. New results obtained at the COSY-11 facility explore the transition region between this low-energy Sigma0 suppression and excess energies of 60 MeV. A first total cross section for elementary antikaon production below the phi threshold has been determined, two orders of magnitude smaller compared to kaon production at the same excess energy.