  We show that when using the underlying positive model structure on symmetric
spectra one obtains cofibrancy conditions for operadic constructions under much
milder hypothesis than one would need for general categories. Our main result
provides such an analysis for a key operation, the "relative composition
product" $\circ_{\mathcal{O}}$ between right and left $\mathcal{O}$-modules
over a spectral operad $\mathcal{O}$, and as a consequence we recover (and
usually strengthen) previous results establishing the Quillen invariance of
model structures on categories of algebras via weak equivalences of operads,
compatibility of forgetful functors with cofibrations and Reedy cofibrancy of
bar constructions.
  Key to the results above are novel cofibrancy results for $n$-fold smash
powers of positive cofibrant spectra (and the relative statement for maps).
Roughly speaking, we show that such $n$-fold powers satisfy a (new) type of
$\Sigma_n$-cofibrancy which can be viewed as "lax $\Sigma_n$-free/projective
cofibrancy" in that it determines a larger class of cofibrations still
satisfying key technical properties of "true $\Sigma_n$-free/projective
cofibrancy."
