  The hadronic kt-spectrum inside one jet is determined including corrections
of relative magnitude sqrt{alpha_s} with respect to the Modified Leading
Logarithmic Approximation (MLLA), at and beyond the limiting spectrum (assuming
an infrared cut-off Q_0 = Lambda_QCD and Q_0 not = Lambda_QCD). The agreement
between our results and preliminary measurements by the CDF collaboration is
impressive, much better than at MLLA, pointing out very small overall
non-perturbative contributions.
