Members of the Syk family of tyrosine kinases arrange Src homology 2 (SH2) domains in tandem to allow the firm binding of immunoreceptor tyrosine-based interaction motifs (ITAMs). While the advantages provided by the bivalency enhanced interactions are evident, the impact on binding specificity is less-clear. For example, the spleen tyrosine kinase (Syk) and the ζ-chain-associated protein kinase (ZAP-70) recognize the consensus sequence pYXXI/L(X)6-8 pYXXI/L with near-identical nanomolar affinity. The nondiscriminatory recognition, on the one hand, poses a specificity challenge for the design of subtype selective protein binders and, on the other hand, raises the question as to how differential activation of Syk and ZAP-70 is ensured when both kinases are co-expressed. Herein, we identified the criteria for the design of binders that specifically address either the Syk or the Zap-70 tSH2 domain. Our approach is based on DNA-programmed spatial screening. Tyrosine-phosphorylated peptides containing the pYXXI/L motif were attached to oligonucleotides and aligned in tandem on a DNA template by means of nucleic acid hybridization. The distance between the pYXXI/L motifs and the orientation of strands were varied. The exploration exposed remarkably different recognition characteristics. While Syk tSH2 has a rather broad substrate scope, ZAP-70 tSH2 required a proximal arrangement of the phosphotyrosine ligands in defined strand orientation. The spatial screen led to the design of mutually selective, DNA-free binders, which discriminate Zap-70 and Syk tSH2 by 1 order of magnitude in affinity.