Heterochromatin formation in Schizosaccharomyces pombe requires the spreading of histone 3 (H3) Lysine 9 (K9) methylation (me) from nucleation centers by the H3K9 methylase, Suv39/Clr4, and the reader protein, HP1/Swi6. To accomplish this, Suv39/Clr4 and HP1/Swi6 have to associate with nucleosomes both nonspecifically, binding DNA and octamer surfaces and specifically, via recognition of methylated H3K9 by their respective chromodomains. However, how both proteins avoid competition for the same nucleosomes in this process is unclear. Here, we show that phosphorylation tunes the nucleosome affinity of HP1/Swi6 such that it preferentially partitions onto Suv39/Clr4's trimethyl product rather than its unmethylated substrates. Preferential partitioning enables efficient conversion from di-to trimethylation on nucleosomes in vitro and H3K9me3 spreading in vivo. Together, our data suggests that phosphorylation of HP1/Swi6 creates a regime that relieves competition with the "read-write" mechanism of Suv39/Clr4 for productive heterochromatin spreading.