The present study gives a comprehensive portrait of the accusatival-passival type of the composite-predicate (or support-verb) construction in the history of Latin. Taking stock of properties shows them to only minimally serve as a touchstone distinguishing between Latin composite predicates and syntagmatically identical verb + direct object constructs. The intricate issue of idiomaticity and the prospects of establishing its parameters are discussed, concluding that although characteristics such as figurativity of the verb or direct-object incorporation indicate this status, the closed corpus of Latin securely allows only for a quantitative parameter, or familiarity, for this kind of a complex predicate. We are looking from the diachronic perspective at individual support verbs, primarily capere and habere, in the evolvement of their function and status—grammatical or lexical-phraseological—as well as at other sets of verbs, figurative ones and verbs otherwise departing from their basic meaning. The support verb emerges as the cardinal constituent of the construct, determining the function of the complex, and as considerably autonomous, being capable of representing, in anaphoric contexts, the entire construction. A reconsideration of the opposition between composite predicates and their monolexematic counterparts brings up again their added value as to exhaustiveness, clarity, perspective, and focus of the message conveyed through a composite predicate.