Isw1 and Chd1 are ATP-dependent nucleosome-spacing enzymes required to establish regular arrays of phased nucleosomes near transcription start sites of yeast genes. Cells lacking both Isw1 and Chd1 have extremely disrupted chromatin, with weak phasing, irregular spacing and a propensity to form close-packed dinucleosomes. The Isw1 ATPase subunit occurs in two different remodeling complexes: ISW1a (composed of Isw1 and Ioc3) and ISW1b (composed of Isw1, Ioc2 and Ioc4). The Ioc4 subunit of ISW1b binds preferentially to the H3-K36me3 mark. Here we show that ISW1b is primarily responsible for setting nucleosome spacing and resolving close-packed dinucleosomes, whereas ISW1a plays only a minor role. ISW1b and Chd1 make additive contributions to dinucleosome resolution, such that neither enzyme is capable of resolving all dinucleosomes on its own. Loss of the Set2 H3-K36 methyltransferase partly phenocopies loss of Ioc4, resulting in increased dinucleosome levels with only a weak effect on nucleosome spacing, suggesting that Set2-mediated H3-K36 trimethylation contributes to ISW1b-mediated dinucleosome separation. The H4 tail domain is required for normal nucleosome spacing but not for dinucleosome resolution. We conclude that the nucleosome spacing and dinucleosome resolving activities of ISW1b and Chd1 are critical for normal global chromatin organisation.