  We report on recent progress in the calculation of $B_K$ using HYP-smeared
improved staggered fermions on the MILC asqtad lattices. We have added
measurements on fine ($a\sim 0.09 $fm) and superfine ($a\sim 0.06 $fm)
ensembles at different values of the light sea quark mass ($a m_\ell$), as well
as increased the statistics on some other ensembles. We find that the results
on the fine lattices show a significantly stronger $am_\ell$ dependence than
those on the superfine and coarse ($a\sim 0.12 $fm) lattices. We discuss
different methods for accounting for these new results when doing the $a
m_\ell$ and continuum extrapolations.
