  We study the existence of cubic quotients of finite-dimensional quasi-normed
spaces, that is, quotients well isomorphic to $\ell_{\infty}^k$ for some $k.$
We give two results of this nature. The first guarantees a proportional
dimensional cubic quotient when the envelope is cubic; the second gives an
estimate for the size of a cubic quotient in terms of a measure of
non-convexity of the quasi-norm.
