We study a positivity condition for the curvature of oriented Riemannian 4-manifolds: The half-P IC condition. It is a slight weakening of the positive isotropic curvature (P IC) condition introduced by M. Micallef and J. Moore. We observe that the half-P IC condition is preserved by the Ricci flow and satisfies a maximality property among all Ricci flow invariant positivity conditions on the curvature of oriented 4-manifolds. We also study some geometric and topological aspects of half-P IC manifolds.