Yeast two-hybrid (Y2H) screenings result in identification of many out-of-frame (OOF) clones that code for short (2-100 amino acids) peptides with no sequence homology to known proteins. We hypothesize that these peptides can reveal common short linear motifs (SLiMs) responsible for their selection. We present a new protocol to address this issue, using an existing SLIM detector (TEIRESIAS) as a base method, and applying filters derived from a mathematical model of SLiM selection in OOF clones. The model allows for initial analysis of likely presence of SLiM(s) in a collection of OOF sequences, assisting investigators with the decision of whether to invest resources in further analysis. If SLiM presence is detected, it estimates the length and number of amino acid residues involved in binding specificity and the amount of noise in the Y2H screen. We demonstrate that our model can double the prediction sensitivity of TEIRESIAS and improve its specificity from 0 to 1.0 on simulated data and apply the model to seven sets of experimentally derived OOF clones. Finally, we experimentally validate one SLiM found by our method, demonstrating its utility.