  We include strong parity-violating contributions to inclusive deep inelastic
scattering (DIS) of longitudinally polarized leptons off an unpolarized target.
At variance with standard results, we obtain nonvanishing parity-violating
structure functions in the case of pure photon exchange. The addition of these
strong parity-violating contributions improves the description of existing
experimental data on DIS parity-violating asymmetries. We find the size of
these contributions small but exhibiting a deviation from zero of about 1.5
$\sigma$. The associated $p$-value is 0.063, indicating that the probability of
making an error by rejecting the hypothesis of no parity-violating
contributions is 6.3\%, which is small but not negligible. Further improvement
on the limit of the strong parity-violation can be expected from the future
SoLID program at Jefferson Lab.
