  In the world without an axion the smallness of $\bar\theta$ may be achieved
due to a spontaneously broken discrete left-right symmetry. We analyze the
radiatively induced \bar\theta in the context of generic left-right symmetric
SUSY models without assuming flavor degeneracy in the squark sector. Left-right
symmetry allows to keep \bar\theta within its present bound only if the
inter-generational mass splitting in the squark sector at the scale of the
left-right symmetry breaking is smaller than 0.5%. We also consider the
naturalness of m_u=0 solution to the strong CP problem in the context of
horizontal flavor symmetries. A strong bound on the combination of the
horizontal charges in the Up quark sector is found in this case.
