Elasticurves present a novel approach to neaten sketches in real-time, resulting in curves that combine smoothness with user-intended detail. Inspired by natural variations in stroke speed when drawing quickly or with precision, we exploit stroke dynamics to distinguish intentional fine detail from stroke noise. Combining inertia and stroke dynamics, elasticurves can be imagined as the trace of a pen attached to the user by an oscillation-free elastic band. Sketched quickly, the elasticurve spatially lags behind the stroke, smoothing over stroke detail, but catches up and matches the input stroke at slower speeds. Connectors, such as lines or circular-arcs link the evolving elasticurve to the next input point, growing the curve by a responsiveness fraction along the connector. Responsiveness is calibrated, to reflect drawing skill or device noise. Elasticurves are theoretically sound and robust to variations in stroke sampling. Practically, they neaten digital strokes in real-time while retaining the modeless and visceral feel of pen on paper.