We describe a simple mechanism for bounding the portion of the plane lying between a quadratic Beizer curve segment and its offset curve at distance d. Instead of comprising one or more partial bounding polygons, our representation consists of only a single approximate offset curve segment, also in quadratic Bezier form. Evaluated on a corpus of real-world curves, this technique avoids 68-99% of antialias-distance queries and 41-96% of brush parameter queries. A proof of correctness is provided.