  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.
