  We examine the possibility of building a natural non-supersymmetric model of
spontaneous CP violation equipped with the Nelson-Barr (NB) mechanism to
address the strong CP problem. Our approach is to utilize a doubly composite
dynamics where the first confinement of the CFT occurs at the scale of
spontaneous CP violation (SCPV) and the second confinement at the TeV scale. A
holographic dual description of this 4D set-up via a warped extra dimension
with three 3-branes provides an explicit realization of this idea.In this
model, radiative corrections to the strong CP phase are well under control, and
the coincidence of mass scales, which we generally encounter in NB models, is
addressed. Our model also provides an explanation to the quark Yukawa
hierarchies, and a solution to the gauge hierarchy problem just as in the usual
Randall-Sundrum model with the Higgs being localized on the TeV brane.
