Chromatin-remodelling complexes (CRCs) mobilize nucleosomes to mediate the access of DNA-binding factors to their sites in vivo. These CRCs contain a catalytic subunit that bears an ATPase/DNA-translocase domain and flanking regions that bind nucleosomal epitopes. A central question is whether and how these flanking regions regulate ATP hydrolysis or the coupling of hydrolysis to DNA translocation, to affect nucleosome-sliding efficiency. ISWI-family CRCs contain the protein ISWI, which uses its ATPase/DNA-translocase domain to pump DNA around the histone octamer to enable sliding. ISWI is positively regulated by two 'activating' nucleosomal epitopes: the 'basic patch' on the histone H4 tail, and extranucleosomal (linker) DNA. Previous work defined the HAND-SANT-SLIDE (HSS) domain at the ISWI carboxy terminus that binds linker DNA, needed for ISWI activity. Here we define two new, conserved and separate regulatory regions on Drosophila ISWI, termed AutoN and NegC, which negatively regulate ATP hydrolysis (AutoN) or the coupling of ATP hydrolysis to productive DNA translocation (NegC). The two aforementioned nucleosomal epitopes promote remodelling indirectly by preventing the negative regulation of AutoN and NegC. Notably, mutation or removal of AutoN and NegC enables marked nucleosome sliding without the H4 basic patch or extranucleosomal DNA, or the HSS domain, conferring on ISWI the biochemical attributes normally associated with SWI/SNF-family ATPases. Thus, the ISWI ATPase catalytic core is an intrinsically active DNA translocase that conducts nucleosome sliding, onto which selective 'inhibition-of-inhibition' modules are placed, to help ensure that remodelling occurs only in the presence of proper nucleosomal epitopes. This supports a general concept for the specialization of chromatin-remodelling ATPases, in which specific regulatory modules adapt an ancient active DNA translocase to conduct particular tasks only on the appropriate chromatin landscape.