  Extending the transverse momentum dependent factorization to thrust dependent
observables entails a series of difficulties, ultimately associated to the
behavior of soft radiation. As a consequence, the definition of the transverse
momentum dependent functions has to be revised, while preserving (and possibly
extending) their universality properties. Moreover, the regularization of the
rapidity divergences generates non trivial correlations between rapidity and
thrust. In this paper, we show how to deal with these correlations in a
consistent treatment of the thrust dependence of $e^+ e^- \to h \, X$ cross
section, where the hadron transverse momentum is measured with respect to the
thrust axis. In this framework all results obtained in the past few years
properly fit together, leading to a remarkable phenomenological description of
the experimental measurements.
