  We study diagonal and transition quark dipole operators in a class of
extended technicolor (ETC) models, taking account of the multiscale nature of
the ETC gauge symmetry breaking and of the mixing among ETC interaction
eigenstates. Because of this mixing, terms involving the lowest ETC scale can
play an important role in dipole operators, and we focus on these terms. We
derive from experiment new correlated constraints on the quark mixing angles
and phases. Our bounds yield information on mixing angles individually in the
up- and down-sectors, for both left- and right-handed quark fields and thus
constrain even quark mixing parameters that do not enter in the CKM matrix.
With phases of order unity, we conclude that these mixing angles are small,
constraining future ETC model building, but plausibly in the range suggested by
the size of the CKM elements. These values still allow substantial deviations
from the standard model predictions, in particular for several CP violating
quantities, including the asymmetries in $b \to s \gamma$ and $B_{d} \to \phi
K_S$, $Re(\epsilon^\prime/\epsilon)$, and the electric dipole moments of the
neutron and the ${}^{199}$Hg atom.
