Saccharomyces cerevisiae Spt6 protein is a conserved chromatin factor with several distinct functional domains, including a natively unstructured 30-residue N-terminal region that binds competitively with Spn1 or nucleosomes. To uncover physiological roles of these interactions, we isolated histone mutations that suppress defects caused by weakening Spt6:Spn1 binding with the spt6-F249K mutation. The strongest suppressor was H2A-N39K, which perturbs the point of contact between the two H2A-H2B dimers in an assembled nucleosome. Substantial suppression also was observed when the H2A-H2B interface with H3-H4 was altered, and many members of this class of mutations also suppressed a defect in another essential histone chaperone, FACT. Spt6 is best known as an H3-H4 chaperone, but we found that it binds with similar affinity to H2A-H2B or H3-H4. Like FACT, Spt6 is therefore capable of binding each of the individual components of a nucleosome, but unlike FACT, Spt6 did not produce endonuclease-sensitive reorganized nucleosomes and did not displace H2A-H2B dimers from nucleosomes. Spt6 and FACT therefore have distinct activities, but defects can be suppressed by overlapping histone mutations. We also found that Spt6 and FACT together are nearly as abundant as nucleosomes, with 24,000 Spt6 molecules, 42,000 FACT molecules, and 75,000 nucleosomes per cell. Histone mutations that destabilize interfaces within nucleosomes therefore reveal multiple spatial regions that have both common and distinct roles in the functions of these two essential and abundant histone chaperones. We discuss these observations in terms of different potential roles for chaperones in both promoting the assembly of nucleosomes and monitoring their quality.