Yeast prions are a powerful model for understanding the dynamics of protein aggregation associated with a number of human neurodegenerative disorders. The AAA+ protein disaggregase Hsp104 can sever the amyloid fibrils produced by yeast prions. This action results in the propagation of "seeds" that are transmitted to daughter cells during budding. Overexpression of Hsp104 eliminates the [PSI+] prion but not other prions. Using biochemical methods we identified Hsp104 binding sites in the highly charged middle domain of Sup35, the protein determinant of [PSI+]. Deletion of a short segment of the middle domain (amino acids 129-148) diminishes Hsp104 binding and strongly affects the ability of the middle domain to stimulate the ATPase activity of Hsp104. In yeast, [PSI+] maintained by Sup35 lacking this segment, like other prions, is propagated by Hsp104 but cannot be cured by Hsp104 overexpression. These results provide new insight into the enigmatic specificity of Hsp104-mediated curing of yeast prions and sheds light on the limitations of the ability of Hsp104 to eliminate aggregates produced by other aggregation-prone proteins.