We revisit the fragmentation processes $g{\to}\chi_{cJ}{+}g$, $g{\to}\eta_{c}{+}g$, $g{\to}J/\psi{+}g{+}g$, and $g{\to}h_c{+}g{+}g$. We argue that the problem of previous calculations was in extending perturbation technique to an essentially nonperturbative region and, on the other hand, in
neglecting important physical phenomena such as the finite size of the bound system and confinement forces. We propose a simple semi-phenomenological model which repairs the physical behavior of the fragmentation functions. Contrary to what was presented previously in the literature, our fragmentation
functions are strictly positive, smooth, and vanish at $z\to 1$.