  We undertake a comprehensive investigation of the properties of the sphaleron
in electroweak theories with two Higgs doublets. We do this in as
model-independent a way as possible: by exploring the physical parameter space
described by the masses and mixing angles of the Higgs particles. If there is a
large split in the masses of the neutral Higgs particles, there can be several
sphaleron solutions, distinguished by their properties under parity and the
behaviour of the Higgs field at the origin. In general, these solutions appear
in parity conjugate pairs and are not spherically symmetric, although the
departure from spherical symmetry is small. Including CP violation in the Higgs
potential can change the energy of the sphaleron by up to 14 percent for a
given set of Higgs masses, with significant implications for the baryogenesis
bound on the mass of the lightest Higgs.
