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The problem of accounting for the quantum degrees of freedom in passing frommassive higher-spin potentials to massless ones and its inverse, the"fattening" of massless tensor potentials of helicity $\pm h$ to their massive$s = |h|$ counterparts, are solved - in a perfectly ghost-free approach - using"string-localized fields". This approach allows to overcome the Weinberg-Wittenimpediment against the existence of massless $|h| \geq 2$ energy-momentumtensors, and to qualitatively and quantitatively resolve the vanDam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, inthe limit $m \to 0$.

Relations between positivity, localization and degrees of freedom: the Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity