The article investigates the ordering of complements in Latin support verb constructions (SVC) of the type bellum inferre or insidias facere with prototypically trivalent verbs, which can either keep or lose the third valency in such constructions. After the brief synopsis of the issues regarding general aspects of the SVCs, the author focuses on the order of the Direct and Indirect objects within the nine constructions (304 occurrences in total) taken from the works of Classical Latin writers. The theoretical background of the analysis applied is the idea of interaction and competition between the three language dimensions, i. e. semantic, pragmatic and deictic-denotative ones, which can determine various orderings of the complements in their relation to each other. On the basis of a previous corpus study concerning the argument structure of Latin trivalent verbs, the author considers the order Direct-Indirect object (DI) as unmarked (neutral), while the opposite order ID as resulting from either special deictic-denotative properties of the arguments or pragmatic factors. As regards the deictic-denotative properties, they depend on the place occupied by the noun or the pronoun in the animacy hierarchy. The promotion of the Indirect object to the priority position is explained by the animacy of its denotatum or by the status of speech act participant, if it is expressed by a personal / reflexive / anaphoric pronoun. The author analyzes the order of the Direct and Indirect objects in the nine support verb constructions selected from the works by Caesar, Cicero and Sallust (304 occurrences in total). The analysis demonstrates that the order ID is attested three times as often as the opposite order DI, because the Indirect objects are usually animate or pronominal in the constructions of this type. In some cases, however, the pragmatic factors such as focus, contrast or emphasis may also influence the ordering. The findings are represented in the table and are followed by the examples.