High-power ultrafast lasers are important for numerous industrial and scientific applications. Current multi-watt systems, however, are based on relatively complex laser concepts, for example using additional intracavity elements for pulse formation. Moving towards a higher level of integration would reduce complexity, packaging, and manufacturing cost, which are important requirements for mass production. Semiconductor lasers are well established for such applications, and optically-pumped vertical external cavity surface emitting lasers (VECSELs) are most promising for higher power applications, generating the highest power in fundamental transverse mode (>20 W) to date. Ultrashort pulses have been demonstrated using passive modelocking with a semiconductor saturable absorber mirror (SESAM), achieving for example 2.1-W average power, sub-100-fs pulse duration, and 50-GHz pulse repetition rate. Previously the integration of both the gain and absorber elements into a single wafer was demonstrated with the MIXSEL (modelocked integrated external-cavity surface emitting laser) but with limited average output power (<200 mW). We have demonstrated the power scaling concept of the MIXSEL using optimized quantum dot saturable absorbers in an antiresonant structure design combined with an improved thermal management by wafer removal and mounting of the 8-µm thick MIXSEL structure directly onto a CVD-diamond heat spreader. The simple straight cavity with only two components has generated 28-ps pulses at 2.5-GHz repetition rate and an average output power of 6.4 W, which is higher than for any other modelocked semiconductor laser.