Quasifree field-driven electron trajectories are a key element of strong-field dynamics. Upon recollisionwith the parent ion, the energy transferred from the field to the electron may be released as attoseconddurationextreme ultaviolet emission in the process of high-harmonic generation. The conventionalsinusoidal driver fields set limitations on the maximum value of this energy transfer and the efficient returnof the launched electron trajectories. It has been predicted that these limits can be significantly exceeded byan appropriately ramped-up cycle shape [L. E. Chipperfield et al., Phys. Rev. Lett. 102, 063003 (2009)].Here, we present an experimental realization of similar cycle-shaped wave forms and demonstrate control of the high-harmonic generation process on the single-atom quantum level via attosecond steering of the electron trajectories. With our improved optical cycles, we boost the field ionization launching the electron trajectories, increase the subsequent field-to-electron energy transfer, and reduce the trajectory duration.We demonstrate, in realistic experimental conditions, 2 orders of magnitude enhancement of the generated extreme ultraviolet flux together with an increased spectral extension. This application, which is only one example of what can be achieved with cycle-shaped high-field light waves, has significant implications for attosecond spectroscopy and molecular self-probing.