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Quantum-dot laser diodes with up to five well-defined electronic shells are fabricated using self-assembled quantum dots (QDs) grown by molecular-beam epitaxy. Shape-engineered stacks of self-aligned QDs with improved uniformity are used to increase the gain in the active region. Lasing is observed in the upper QD shells for small-gain media, and progresses towards the QD ground states for longer cavity lengths. We obtained at 77 K thresholds of for a 2 mm cavity lasing in the first excited state (p shell), and for a 1 mm cavity lasing in (d shell). At 300 K for a 1 mm cavity, is with lasing in (f shell).