A double-sided milling insert for high feed milling of metal workpieces includes upper and lower faces facing in opposite directions and convex clearance surfaces extending between the upper and lower faces. Each one of the faces includes a recessed support surface. The support surfaces are substantially parallel to each other and have a cavity therein for receiving a fastening device. Intersections of the convex clearance surfaces with the upper and lower faces form convex cutting edges when seen in a plan view. A rake face is provided adjacent the convex cutting edges. Each convex cutting edge is concave when seen in a side view and includes a substantially straight cutting edge portion on each side of a curved cutting edge portion when seen in plan view. A milling tool with a plurality of such inserts and a method of high feed milling using this tool are also disclosed.