Achieving accurate arbitrary frequency excursions with a laser can be quite a technical challenge, especially when steep slopes (GHz/µs) are required, due to both deterministic and stochastic frequency fluctuations. In this work we present a multistage correction combining four techniques: pre-distorsion of the laser modulation, iterative correction, opto-electronic feedback loop, and feed-forward correction. This combination allows us 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 multistage 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 multistage 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 gigahertz-scale frequency excursions.