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Achieving accurate arbitrary frequency excursions with a laser can be quite a technical challenge, especially when steep slopes (GHz/$\mu$s) are required, due to both deterministic and stochastic frequency fluctuations. In this work we present a multi-stage correction combining four techniques: pre-distorsion of the laser modulation, iterative correction, opto-electronic feedback loop and feed-forward correction. This combination allows not only to compensate for the non-instantaneous response of the laser to an input modulation, but also to correct in real time the stochastic frequency fluctuations. We implement this multi-stage architecture on a commercial DBR laser and verify its efficiency, first with monochromatic operation and second with highly demanding frequency excursions. We demonstrate that our multi-stage correction not only enables a strong reduction of the laser linewidth, but also allows steep frequency excursions with a relative RMS frequency error well below $1$%, and a laser spectral purity consistently better than $100$~kHz even in the midst of GHz-scale frequency excursions., Comment: 20 pages, 17 figures