The Tat protein of immunodeficiency viruses is the main activator of viral gene expression. By binding specifically to its cognate site, the transactivator response element (TAR), Tat mediates a strong induction of the production of all viral transcripts. In seeking a new chemical solution to inhibiting viral protein-RNA interactions, we recently identified inhibitors of the viral Tat protein from the bovine immunodeficiency virus (BIV) using conformationally constrained beta-hairpin peptidomimetics. We identified a micromolar ligand, called BIV2, and the structure of its complex with BIV TAR was determined by NMR. In this work, we demonstrate that this chemistry can rapidly yield highly potent and selective ligands. On the basis of the structure, we synthesized and assayed libraries of mutant peptidomimetics. Remarkably, we were able in just a few rounds of design and synthesis to discover nanomolar inhibitors of the Tat-TAR interaction in BIV that selectively bind the BIV TAR RNA compared to RNA structures as closely related as the HIV-1 TAR or RRE elements. The molecular recognition principles developed in this study have been exploited in discovering related peptidomimetic inhibitors of the Tat-TAR interaction in HIV-1.