The absence of sizeable CP violation in the strong sector is a long standing puzzle. A class of solutions to this problem rely on a global U(1) symmetry that is anomalous with QCD. These solutions lead to robust low-energy predictions, for example a massless up quark or a light axion. I will present simple extensions to such solutions which can dramatically change these low-energy predictions. In our models, contributions from small instantons play a significant role in affecting the low-energy physics while preserving the solution to the strong CP problem.