We consider highly specific protein-protein interactions in proteomes of simple model proteins. We are inspired by the work of Zarrinpar et al (2003 Nature 426 676). They took a binding domain in a signalling pathway in yeast and replaced it with domains of the same class but from different organisms. They found that the probability of a protein binding to a protein from the proteome of a different organism is rather high, around one half. We calculate the probability of a model protein from one proteome binding to the protein of a different proteome. These proteomes are obtained by sampling the space of functional proteomes uniformly. In agreement with Zarrinpar et al we find that the probability of a protein binding a protein from another proteome is rather high, of order one tenth. Our results, together with those of Zarrinpar et al, suggest that designing, say, a peptide to block or reconstitute a single signalling pathway, without affecting any other pathways, requires knowledge of all the partners of the class of binding domains the peptide is designed to mimic. This knowledge is required to use negative design to explicitly design out interactions of the peptide with proteins other than its target. We also found that patches that are required to bind with high specificity evolve more slowly than those that are required only to not bind to any other patch. This is consistent with some analysis of sequence data for proteins engaged in highly specific interactions.