Near-transform-limited subpicosecond pulses at 1.56 μm were generated from an optically pumped InP-based vertical-external-cavity surface-emitting laser (VECSEL) passively mode-locked at 2 GHz repetition rate with a fast InGaAsNSb/GaAs semiconductor saturable absorber mirror (SESAM). The SESAM microcavity resonance was adjusted via a selective etching of phase layers specifically designed to control the magnitude of both the modulation depth and the intracavity group delay dispersion of the SESAM. Using the same VECSEL chip, we observed that the mode-locked pulse duration could be reduced from several picoseconds to less than 1 ps with a detuned resonant SESAM.