We report significant improvement in the performance of TEM00 alexandrite laser operation by employing high power fibre-coupled red diode pumping, novel cavity design, and active direct Shack-Hartmann wavefront sensor measurement of pump-induced lensing. We demonstrate 12.7 W of laser power in low-order (𝑀2∼5) mode operation from a compact double-end-pumped cavity, and with novel cavity design, a record power of 7.4 W in TEM00 operation with excellent beam quality (𝑀2≤1.1). With single-end pumping, laser power of 4.7 W (𝑀2∼1.3) was achieved with slope efficiencies as high as 54.9 %; a record efficiency for red-diode-pumped alexandrite. Using a birefringent filter, continuous laser wavelength tuning from 725-808 nm is achieved in diffraction-limited TEM00 mode, with laser power of 4.7 W at 765 nm, and >1 W across 730-805 nm, which is a higher tunable power than any other directly diode-pumped vibronic laser, to the best of our knowledge.