  To reconstruct dark energy models the redshift $z_{eq}$, marking the end of
radiation era and the beginning of matter-dominated era, can play a role as
important as $z_{t}$, the redshift at which deceleration parameter experiences
a signature flip. To implement the idea we propose a variable equation of state
for matter that can bring a smooth transition from radiation to
matter-dominated era in a single model. A popular $\Lambda \propto \rho$ dark
energy model is chosen for demonstration but found to be unacceptable. An
alternative $\Lambda \propto \rho a^{3}$ model is proposed and found to be more
close to observation.
