Objects in freely-drawn sketches often have no spatial or temporal separation, making object recognition difficult. We present a two-step stroke-grouping algorithm that first classifies individual strokes according to the type of object to which they belong, then groups strokes with like classifications into clusters representing individual objects. The first step facilitates clustering by naturally separating the strokes, and both steps fluidly integrate spatial and temporal information. Our approach to grouping is unique in its formulation as an efficient classification task rather than, for example, an expensive search task. Our single-stroke classifier performs at least as well as existing single-stroke classifiers on text vs. nontext classification, and we present the first three-way single-stroke classification results. Our stroke grouping results are the first reported of their kind; our grouping algorithm correctly groups between 86% and 91% of the ink in diagrams from two domains, with between 69% and 79% of shapes being perfectly clustered.