The spring wheat 'Canthatch' has been shown to suppress stem rust resistance genes in the background due to the presence of a suppressor gene located on the long arm of chromosome 7D. However, it is unclear whether the suppressor also suppresses resistance genes against leaf rust and stripe rust. In this study, we investigated the specificity of the resistance suppression. To determine whether the suppression is genome origin specific, chromosome location specific, or rust species or race specific, we introduced 11 known rust resistance genes into the Canthatch background, including resistance to leaf, stripe, or stem rusts, originating from A, B, or D genomes and located on different chromosome homologous groups. F1 plants of each cross were tested with the corresponding rust race, and the infection types were scored and compared with the parents. Our results show that the Canthatch 7DL suppressor only suppressed stem rust resistance genes derived from either the A or B genome, and the pattern of the suppression is gene specific and independent of chromosomal location.