  This is the sequel to arXiv:math/0001089. In this paper, we complete the
promised description of moduli of abelian surfaces of low degree, covering the
cases of degree (1,12), (1,14), (1,16), (1,18) and (1,20). In each case, we
describe birational models for the moduli space of abelian surfaces with
polarization of the given degree and either a level structure, or what we call
a partial level structure. In every case, the moduli space is rational or
unirational. In additional, several new Calabi-Yau threefolds fibred in abelian
surfaces are described.
