A double-sided cutting insert with a plurality of indexable convex cutting edges can have a top face and a bottom face, at least three convex cutting edges on each face connected by at least three nose corners, at least three peripheral side surfaces extending from each face toward a virtual middle plane; and a common lateral seating surface on each peripheral side surface. Each convex cutting edge can have at least a curved cutting edge region, and can further have a primary substantially straight cutting edge region intermediate the curved cutting edge region and the nose corner. Each peripheral side surface can further have a primary planar facet associated with the primary substantially straight cutting edge, and each face may also be single-handed in same direction.