A “Stroke Untangler” composes handwritten messages from handwritten strokes representing overlapping letters or partial letter segments are drawn on a touchscreen device or touch-sensitive surface. These overlapping strokes are automatically untangled and then segmented and combined into one or more letters, words, or phrases. Advantageously, segmentation and composition is performed without requiring user gestures, timeouts, or other inputs to delimit characters within words, and without using handwriting recognition-based techniques to guide untangling and composing of the overlapping strokes to form characters. In other words, the user draws multiple overlapping strokes. Those strokes are then automatically segmented and combined into one or more corresponding characters. Text recognition of the resulting characters is then performed. Further, the segmentation and combination is performed in real-time, thereby enabling real-time rendering of the resulting characters in a user interface window. A related drawing mode enables entry of drawings in combination with the handwritten characters.