We report on the development of a new generation of high-power ultrashort pulse quantum-dot lasers with tapered gain section. Two device designs are proposed and fabricated, with different total lengths and absorber-to-gain-section length-ratios. These designs have been informed by numerical simulations of the dynamic mode-locking regimes and their dependence on the structural parameters. One device design demonstrated a record-high peak power of 17.7 W with 1.26 ps pulse width and a second design enabled the generation of a Fourier-limited 672 fs pulse width with a peak power of 3.8 W. A maximum output average power of 288 mW with 28.7 pJ pulse energy was also attained. In addition, the integrated timing jitter of 2.6 ps and far-field patterns are demonstrated.