While selective inhibition is one of the key assets for a small molecule drug, many diseases can only be tackled by simultaneous inhibition of several proteins. An example where achieving selectivity is especially challenging are ligands targeting human kinases. This difficulty arises from the high structural conservation of the kinase ATP binding sites, the area targeted by most inhibitors. We investigated the possibility to identify novel small molecule ligands with pre-defined binding profiles for a series of kinase targets and anti-targets by in silico docking. The candidate ligands originating from these calculations were assayed to determine their experimental binding profiles. Compared to previous studies, the acquired hit rates were low in this specific setup, which aimed at not only selecting multi-target kinase ligands, but also designing out binding to anti-targets. Specifically, only a single profiled substance could be verified as a sub-micromolar, dual-specific EGFR/ErbB2 ligand that indeed avoided its selected anti-target BRAF. We subsequently re-analyzed our target choice and in silico strategy based on these findings, with a particular emphasis on the hit rates that can be expected from a given target combination. To that end, we supplemented the structure-based docking calculations with bioinformatic considerations of binding pocket sequence and structure similarity as well as ligand-centric comparisons of kinases. Taken together, our results provide a multi-faceted picture of how pocket space can determine the success of docking in multi-target drug discovery efforts.