We report on tailoring ionization-induced injection in laser wakefield acceleration so that the electron injection process is self-truncating following the evolution of the plasma bubble. Robust generation of high-quality electron beams with shot-to-shot fluctuations of the beam parameters better than 10% is presented in detail. As a novelty, the scheme was found to enable well-controlled yet simple tuning of the injected charge while preserving acceleration conditions and beam quality. Quasi-monoenergetic electron beams at several 100 MeV energy and 15% relative energy spread were routinely demonstrated with a total charge of the monoenergetic feature reaching 0.5 nC. Finally these unique beam parameters, suggesting unprecedented peak currents of several 10 kA, are systematically related to published data on alternative injection schemes.