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Future redshift-drift measurements will be crucial to probe the so-called "redshift desert", thus providing a new tool for cosmological studies. In this paper we quantify the ability of a future measurement of the redshift-drift signal by a CODEX-like spectrograph to constrain a phenomenological parametrization of dynamical dark energy, specifically by obtaining constraints on w(0) and w(a). We also demonstrate that if used alongside CMB data, the redshift-drift measurements will be able to break degeneracies between expansion parameters, thus greatly improving cosmological constraints.