Let a: Sl ->S2 be a C2 immersion with length L and total curvature K . If a is regularly homotopic to a circle traversed once then L2 + K2 > 4n2 with equality if and only if a is a circle traversed once. If a has nonnegative geodesic curvature and multiple points then L + K > An with equality if and only if a is a great circle traversed twice.