Optically pumped vertical external cavity surface emitting lasers (OP-VECSELs) evolved to high-power laser sources offering excellent beam-quality, wavelength flexibility and low-noise properties in a compact and simple cavity. Passively modelocked with a semiconductor saturable absorber mirror (SESAM), VECSELs demonstrated fs-pulses with multi-Watt average output powers at gigahertz repetition rates. Electrical pumping (EP) is an obvious step to make these semiconductor lasers even more compact and suitable for chip integration, potentially enabling access to applications such as data communication or optical clocking. With SESAMmodelocked EP-VECSELs, 57-ps pulses with an average output power of 40 mW and 9.5-ps pulses with 7.6 mW have been obtained. However, due to the intrinsic trade-off between electrical and optical properties in the design of EPVECSELs, short pulses at high average output power are difficult to achieve. This challenge was previously addressed in our theoretical guidelines for power scaling and modelocking optimization and later experimentally verified. Here, we report on the successful implementation of an improved design and fabrication scheme for EP-VECSELs, grown and fabricated at ETH Zurich. These lasers enabled a further decrease in pulse duration to 7.3 ps while increasing the average output power to 13.1 mW at 1.46-GHz repetition rate. The shortest pulse duration measured was 6.3 ps with an average power of 6.2 mW. In addition to the modelocking experiments, we present a thorough cw-characterization of our EP-VECSELs of different sizes and in different cavity configurations, pointing out the inevitable trade-off between high-power multi-mode and low-power single-mode operation limiting the modelocking performance.