The article focuses on the characteristics and uses of supplementive clauses in modern texts translated from French into Slovene. Since existing grammatical descriptions of these clauses are vague and often illustrated with examples of non-restrictive postmodification or nonessential appositive phrases, we first compare the three types of clauses and propose for each a more restricted definition in order to avoid their further confusion. The analysis shows that participial supplementive clauses predominate in Slovene translations over the adjectival and gerundial ones. In newspaper articles, they are usually placed after the antecedent, whereas in novels they often keep the same sentence-initial position as in the source texts. In the latter examples, inconsistencies in the use of commas have been discovered, which is why we should thoroughly examine the use of supplementive clauses in original contemporary Slovene texts and consider including the findings in future grammatical descriptions.