The La-related proteins (LARPs) form a diverse group of RNA-binding proteins characterized by the possession of a composite RNA binding unit, the La module. The La module comprises two domains, the La motif (LaM) and the RRM1, which together recognize and bind to a wide array of RNA substrates. Structural information regarding the La module is at present restricted to the prototypic La protein, which acts as an RNA chaperone binding to 3' UUUOH sequences of nascent RNA polymerase III transcripts. In contrast, LARP6 is implicated in the regulation of collagen synthesis and interacts with a specific stem-loop within the 5' UTR of the collagen mRNA. Here, we present the structure of the LaM and RRM1 of human LARP6 uncovering in both cases considerable structural variation in comparison to the equivalent domains in La and revealing an unprecedented fold for the RRM1. A mutagenic study guided by the structures revealed that RNA recognition requires synergy between the LaM and RRM1 as well as the participation of the interdomain linker, probably in realizing tandem domain configurations and dynamics required for substrate selectivity. Our study highlights a considerable complexity and plasticity in the architecture of the La module within LARPs.