  Given a closed contact 3-manifold with a compatible Riemannian metric, we
show that if the sectional curvature is 1/4-pinched, then the contact structure
is universally tight. This result improves the Contact Sphere Theorem in
[EKM12], where a 4/9-pinching constant was imposed. Some tightness results on
positively curved contact open 3-manifold are also discussed.
