The problem of accounting for the degrees of freedom in passing from massive spin to massless helicity degrees of freedom and its inverse, the "fattening" of massless tensor fields to their massive $s = |h|$ counterparts, are solved using "string-localized fields". This approach allows to overcome the Weinberg-Witten impediment against the existence of massless $|h|\geq 2$ energy-momentum tensors, and to replace the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, by a continuous limit $m \to 0$.