Laser-plasma accelerators (LPAs) 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 LPAs. Start-to-end simulations demonstrate the efficacy of such post-acceleration phase-space manipulations and the potential to reduce current state-of-the-art energy spread and jitter from $1%$ to $0.10%$ and $0.024%$, respectively, closing the beam-quality gap to conventional acceleration schemes.
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