The La protein binds the 3' ends of many newly synthesized noncoding RNAs, protecting these RNAs from nucleases and influencing folding, maturation, and ribonucleoprotein assembly. Although 3' end binding by La involves the N-terminal La domain and adjacent RNA recognition motif (RRM), the mechanisms by which La stabilizes diverse RNAs from nucleases and assists subsequent events in their biogenesis are unknown. Here we report that a conserved feature of La proteins, an intrinsically disordered C terminus, is required for the accumulation of certain noncoding RNA precursors and for the role of the Saccharomyces cerevisiae La protein Lhp1p in assisting formation of correctly folded pre-tRNA anticodon stems in vivo. Footprinting experiments using purified Lhp1p reveal that the C terminus is required to protect a pre-tRNA anticodon stem from chemical modification. Although the C terminus of Lhp1p is hypersensitive to proteases in vitro, it becomes protease-resistant upon binding pre-tRNAs, U6 RNA, or pre-5S rRNA. Thus, while high affinity binding to 3' ends requires the La domain and RRM, a conformationally flexible C terminus allows La to interact productively with a diversity of noncoding RNA precursors. We propose that intrinsically disordered domains adjacent to well characterized RNA-binding motifs in other promiscuous RNA-binding proteins may similarly contribute to the ability of these proteins to influence the cellular fates of multiple distinct RNA targets.