Nucleosome assembly proteins (Naps) influence chromatin dynamics by directly binding to histones. Here we provide a comprehensive structural and biochemical analysis of a Nap protein from Caenorhabditis elegans (CeNap1). CeNap1 naturally lacks the acidic N-terminal tail and has a short C-terminal tail compared to many other Nap proteins. Comparison of CeNap1 with full length and tail-less constructs of Saccharomyces cerevisiae Nap1 uncovers the role of these tails in self-association, histone binding, and Nap competition with DNA for H2A-H2B. We find that the presence of tails influences the stoichiometry of H2A-H2B binding and is required to complete the interactions between H2A-H2B and DNA. The absolute stoichiometry of the Nap protein and H2A-H2B complex is 2:1 or 2:2, with only a very small population of higher-order oligomers occurring at 150 mM NaCl. We also show that H3-H4 binds differently than H2A-H2B and that an (H3-H4)2 tetramer can simultaneously bind two Nap2 protein homodimers.