Hyperon production in the threshold region was studied in the reaction pp → K + Λp using the time-of-flight spectrometer COSY-TOF. Exclusive data, covering the full phase-space, were taken at the three different beam momenta of p beam = 2.95, 3.20 and 3.30 GeV/c, corresponding to excess energies of ε = 204, 285 and 316 MeV, respectively. Total cross-sections were deduced for the three beam momenta to be 23.9 ± 0.8 ± 2.0 µb, 28.4 ± 1.3 ± 2.2 µb and 35.0 ± 1.3 ± 3.0 µb. Differential observables including Dalitz plots were obtained. The analysis of the Dalitz plots reveals a strong influence of the