A fundamental question in RNA folding is the mechanism of thermodynamic stability. We investigated the equilibrium folding of a series of sequence variants in which one to three motifs of a 255-nucleotide mesophilic ribozyme were substituted with the corresponding motifs from its thermophilic homologue. Substitution of three crucial motifs individually or in groups results in a continual increase in the stability and folding cooperativity in a stepwise fashion. We find an unexpected relationship between stability and folding cooperativity. Without changing the folding cooperativity, RNAs having a similar native structure can only achieve moderate change in stability and likewise, without changing stability, RNAs having a similar native structure can only achieve moderate change in folding cooperativity. This intricate relationship must be included in the predictions of tertiary RNA stability.