RNAs with interesting secondary and tertiary structures tend to melt in several broad and overlapping transitions over a wide temperature range, and it has been consequently difficult to resolve the thermodynamics of individual unfolding steps. In the case that a ligand selectively binds a single folded state of the RNA, it is possible to obtain reliable thermodynamic parameters for both RNA unfolding and RNA-ligand binding simply from the hyperchromicity of RNA denaturation. The analysis procedure involves fitting a three-dimensional surface to absorbance data collected as a function of both temperature and ligand concentration. Analysis of the unfolding of a fragment of the large subunit ribosomal RNA (Escherichia coli sequence 1051 to 1109) is presented; both an antibiotic (thiostrepton) and ammonium ion specifically stabilize a tertiary structure within this RNA. A consistent set of thermodynamic parameters (delta H and tm) for the first two sequentially linked unfolding transitions is obtained from the experiments, and the binding constants obtained for the two ligands are consistent with other independent measurements. The approach is applicable to a variety of RNAs that specifically bind proteins, antibiotics, ions or other ligands.