  We revisit the topic of triple-product asymmetries which probe CP violation
through differential distributions. We construct distributions with
well-defined discrete symmetry properties and characterize the asymmetries
formed upon them. It is stressed that the simplest asymmetries may not be
optimal. We explore systematic generalizations having limited reliance on the
process dynamics and phase-space parametrization. They exploit larger fractions
of the information contained in differential distributions and may lead to
increased sensitivities to CP violation. Our detailed treatment of the case of
spinless four-body decays paves the way for further experimental studies.
