  Nelson-Barr models solve the strong CP problem based on spontaneous CP
violation and generically requires vector-like quarks (VLQs) mixing with
standard quarks to transmit the CP violation. We devise an explicit
parametrization for the case of two VLQs of either down-type or up-type and
quantitatively study several aspects including the hierarchy of the VLQ Yukawas
and their irreducible contribution to $\bar{\theta}$. In particular, with the
use of the parametrization, we show that a big portion of the parameter space
for two up-type VLQs at the TeV scale is still allowed by the constraint on
$\bar{\theta}$, although this case had been previously shown to be very
restricted based on estimates.
