  We explore the effects of quantum mechanical squeezing on the nonequilibrium
thermodynamics of a coherent heat engine with squeezed reservoirs coupled to a
squeezed cavity. We observe that the standard known phenomenon of
flux-optimization beyond the classical limit with respect to quantum coherence
is destroyed in presence of squeezing. Under extreme nonequilibrium conditions,
the flux is rendered independent of squeezing. The efficiency at maximum power
(EMP) obtained by optimizing the cavity's squeezing parameter is greater than
what was predicted by Curzon and Ahlborn even in the absence of reservoir
squeezing. The EMP with respect to the either of reservoirs' squeezing
parameters is surprisingly equal and linear in $\eta_C$ with a slope unequal to
the universally accepted slope, 1/2. The slope is found to be proportional to
the dissipation into the cavity mode and an intercept equal to a specific
numerical value of the engine's efficiency.
