Bromodomains are protein modules adopting conserved helix bundle folds. Some bromodomain-containing proteins, such as ATPase family AAA domain-containing protein 2 (ATAD2), isoform A, have attracted much interest because they are overexpressed in many types of cancer. Bromodomains bind to acetylated lysine residues on histone tails and thereby facilitate the reading of the histone code. Epigenetic regulators in general have been implicated as indicators, mediators, or causes of a large number of diseases and disorders. To interfere with or modulate these processes, it is therefore of fundamental interest to understand the molecular mechanisms by which epigenetic regulation occurs. Here, we present results from molecular dynamics simulations of a doubly acetylated histone H4 peptide bound to the bromodomain of ATAD2 (hereafter referred to as ATAD2A). These simulations revealed how the flexibility of ATAD2A's major loop, the so-called ZA loop, creates an adaptable interface that preserves the disorder of both peptide and loop in the bound state. We further demonstrate that the binding involves an almost identical average pattern of interactions irrespective of which acetyl mark is inserted into the pocket. In conjunction with a likely mechanism of electrostatically driven recruitment, our simulation results highlight how the bromodomain is built toward promiscuous binding with low specificity. In conclusion, the simulations indicate that disorder and electrostatic steering function jointly to recruit ATAD2A to the histone core and that these fuzzy interactions may promote cooperativity between nearby epigenetic marks.