  Let 1 \le p < q \le 2 and let M be any von Neumann algebra. We use recent
techniques from free harmonic analysis to construct a completely isomorphic
embedding of Lq(M) (equipped with its natural operator space structure) into
Lp(A) for some sufficiently large von Neumann algebra A. We show that
hyperfiniteness and the QWEP are preserved in our construction.
