  We explore charged-Higgs cp-violating effects in a specific type III
two-Higgs doublet model which is theoretically attractive as it accommodates
the large mass of the top quark in a natural fashion. Two new CP-violating
phases arise from the right-handed up quark sector. We consider CP violation in
both neutral and charged B decays. Some of the important findings are as
follows. 1) Large direct-CP asymmetry is found to be possible for B+- to psi/J
K+-. 2) Sizable D-anti-D mixing effect at the percent level is found to be
admissible despite the stringent constraints from the data on K-anti-K mixing,
b to s gamma and B to tau nu decays. 3) A simple but distinctive CP asymmetry
pattern emerges in decays of B_d and B_s mesons, including B_d to psi/J K_S, D+
D-, and B_s to D_s+ D_s-, psi eta/eta^prime, psi/J K_S. 4) The effect of
D-anti-D mixing on the CP asymmetry in B+- to D/anti-D K+- and on the
extraction of the angle gamma of the unitarity triangle from such decays can be
significant.
