  A shortcoming of current binary black-hole initial data is the generation of
spurious gravitational radiation, so-called junk radiation, when they are
evolved. This problem is a consequence of an oversimplified modeling of the
binary's physics in the initial data. Since junk radiation is not
astrophysically realistic, it contaminates the actual waveforms of interest and
poses a numerical nuisance. The work here presents a further step towards
mitigating and understanding the origin of this issue, by incorporating
post-Newtonian results in the construction of constraint-satisfying binary
black-hole initial data. Here we focus on including realistic tidal
deformations of the black holes in the initial data, by building on the method
of superposing suitably chosen black hole metrics to compute the conformal
data. We describe the details of our initial data for an equal-mass and
nonspinning binary, compute the subsequent relaxation of horizon quantities in
evolutions, and quantify the amount of junk radiation that is generated. These
results are contrasted with those obtained with the most common choice of
conformally flat (CF) initial data, as well as superposed Kerr-Schild (SKS)
initial data. We find that when realistic tidal deformations are included, the
early transients in the horizon geometries are significantly reduced, along
with smaller deviations in the relaxed black hole masses and spins from their
starting values. Likewise, the junk radiation content in the $l=2$ modes is
reduced by a factor of $\sim$1.7 relative to CF initial data, but only by a
factor of $\sim$1.2 relative to SKS initial data. More prominently, the junk
radiation content in the $3\leq l\leq8$ modes is reduced by a factor of $\sim$5
relative to CF initial data, and by a factor of $\sim$2.4 relative to SKS
initial data.
