ISWI proteins form the catalytic core of a subset of ATP-dependent chromatin remodeling activities in eukaryotes from yeast to man. Many of these complexes have been found to reposition nucleosomes but with different directionalities. We find that the yeast Isw1a, Isw2, and Chd1 enzymes preferentially move nucleosomes toward more central locations on short DNA fragments whereas Isw1b does not. Importantly, the inherent positioning properties of the DNA play an important role in determining where nucleosomes are relocated to by all of these enzymes. However, a key difference is that the Isw1a, Isw2, and Chd1 enzymes are unable to move nucleosomes to positions closer than 15 bp from a DNA end, whereas Isw1b can. We also find that there is a correlation between the inability of enzymes to move nucleosomes close to DNA ends and the preferential binding to nucleosomes bearing linker DNA. These observations suggest that the accessibility of linker DNA together with the positioning properties of the underlying DNA play important roles in determining the outcome of remodeling by these enzymes.