In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted ℐ _α ) were studied. Such minimizers were called forward ℐ _α -projections. Here, a complementary class of minimization problems leading to the so-called reverse ℐ _α -projections are studied. Reverse ℐ _α -projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (α > 1) and in constrained compression settings (α <; 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse ℐ _α -projection into a forward ℐ _α -projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.