  The polar behavior of double perovskite (Bi,Pb)ZnNbO$_6$ and (Bi,Sr)ZnNbO$_6$
was investigated using first principles density functional calculations within
the local density approximation. These materials have both $A$-site size
disorder and ions with sterochemical activity. We found a strong ferroelectric
distortion in both materials. The polarization of the Pb material is $>$80
$\mu$C/cm$^2$ along the rhombohedral direction and the Sr based material is
only slightly inferior. The high polarization results mainly from a large
off-centering of Bi and the large Born effective charge of Nb, which yields a
large contribution polarization although the Nb off-centers by a smaller
amount. Neither of these materials favors a tetragonal state, and therefore
solid solutions with PbTiO$_3$ may show morphotoropic phase boundaries.
