  Solutions to strong CP based on chiral structure have been subject to the
most careful scrutiny and critique. Basic theoretical issues include hierarchy
and fine-tuning problems, quality and genericity of symmetries, and
compatibility with solutions to the electroweak hierarchy problem. We study the
similar set of challenges for solutions to strong CP based on spontaneous CP
violation and the Nelson-Barr mechanism. Some of our observations have appeared
in the literature previously, and others are new; our purpose is to collect and
analyze the issues as a whole and provide an assessment of the most plausible
settings for the Nelson-Barr solution.
