Self-propagating beta-sheet-rich protein aggregates are implicated in a wide range of protein-misfolding phenomena, including amyloid diseases and prion-based inheritance. Two properties have emerged as common features of amyloids. Amyloid formation is ubiquitous: many unrelated proteins form such aggregates and even a single polypeptide can misfold into multiple forms--a process that is thought to underlie prion strain variation. Despite this promiscuity, amyloid propagation can be highly sequence specific: amyloid fibres often fail to catalyse the aggregation of other amyloidogenic proteins. In prions, this specificity leads to barriers that limit transmission between species. Using the yeast prion [PSI+], we show in vitro that point mutations in Sup35p, the protein determinant of [PSI+], alter the range of 'infectious' conformations, which in turn changes amyloid seeding specificity. We generate a new transmission barrier in vivo by using these mutations to specifically disfavour subsets of prion strains. The ability of mutations to alter the conformations of amyloid states without preventing amyloid formation altogether provides a general mechanism for the generation of prion transmission barriers and may help to explain how mutations alter toxicity in conformational diseases.