  This short note has a twofold purpose:
  (i) to solve the question that motivates a recent paper of D. Popa on
multilinear variants of Pietsch's composition theorem for absolutely summing
operators. More precisely, we remark that there is a natural perfect extension
of Pietsch's composition theorem to the multilinear and polynomial settings.
This fact was overlooked in the aforementioned paper;
  (ii) to investigate extensions of some results of the aforementioned paper
for particular situations, mainly by exploring cotype properties of the spaces
involved.
