  We determine the jet vertex for Mueller-Navelet jets and forward jets in the
small-cone approximation for two particular choices of jet algoritms: the kt
algorithm and the cone algorithm. These choices are motivated by the extensive
use of such algorithms in the phenomenology of jets. The differences with the
original calculations of the small-cone jet vertex by Ivanov and Papa, which is
found to be equivalent to a formerly algorithm proposed by Furman, are shown at
both analytic and numerical level, and turn out to be sizeable. A detailed
numerical study of the error introduced by the small-cone approximation is also
presented, for various observables of phenomenological interest. For values of
the jet "radius" R=0.5, the use of the small-cone approximation amounts to an
error of about 5% at the level of cross section, while it reduces to less than
2% for ratios of distributions such as those involved in the measure of the
azimuthal decorrelation of dijets.
