  We study how strong mechanical squeezing (beyond 3 dB) can be achieved
through reservoir engineering in an optomechanical system which is far from the
resolved-sideband regime. In our proposed setup, the effect of unwanted
counter-rotating terms is suppressed by quantum interference from two auxiliary
cavities. In the weak coupling regime we develop an analytical treatment based
on the effective master equation approach, which allows us to obtain explicitly
the condition of maximum squeezing.
