Glycan-binding proteins are commonly used as analytical reagents to detect the levels of specific glycan structures in biological samples. A detailed knowledge of the specificities of glycan-binding proteins is required for properly interpreting their binding data. A powerful technology for characterizing glycan-binding specificity is the glycan array. However, the interpretation of glycan-array data can be difficult due to the complex fine specificities of certain glycan-binding proteins. We developed a systematic approach, called outlier-motif analysis, for extracting fine-specificity information from glycan-array data, and we applied the method to the study of four commonly used lectins: two mannose binders (concanavalin A and Lens culinaris) and two galactose binders (Bauhinia purpurea and peanut agglutinin). The study confirmed the known, primary specificity of each lectin and also revealed new insights into their binding preferences. Lens culinaris's main specificity may be non-terminal, α-linked mannose with a single linkage at its 2' carbon, which is more restricted than previous definitions. We found broader specificity for bauhinea purpurea (BPL) than previously reported, showing that BPL can bind terminal N-acetylgalactosamine (GalNAc) and penultimate β-linked galactose under certain limitations. Peanut agglutinin may bind terminal Galβ1,3Gal, a glycolipid motif, in addition to terminal Galβ1,3GalNAc, a common O-linked glycoprotein motif. These results could be used to more accurately interpret data obtained using these well-studied lectins. Furthermore, this study demonstrates a systematic and general approach for extracting fine-specificity information from glycan-array data.