  Laser-plasma accelerators outperform current radiofrequency technology in
acceleration strength by orders of magnitude. Yet, enabling them to deliver
competitive beam quality for demanding applications, particularly in terms of
energy spread and stability, remains a major challenge. In this Letter, we
propose to combine bunch decompression and active plasma dechirping for
drastically improving the energy profile and stability of beams from
laser-plasma accelerators. Realistic start-to-end simulations demonstrate the
potential of these post-acceleration phase-space manipulations for
simultaneously reducing an initial energy spread and energy jitter of
$\sim1$-$2\%$ to ${\lesssim} 0.1 \%$, closing the beam-quality gap to
conventional acceleration schemes.
