We qualify the entanglement of arbitrary mixed states of bipartite quantum
systems by comparing global and marginal mixednesses quantified by different
entropic measures. For systems of two qubits we discriminate the class of
maximally entangled states with fixed marginal mixednesses, and determine an
analytical upper bound relating the entanglement of formation to the marginal
linear entropies. This result partially generalizes to mixed states the
quantification of entaglement with marginal mixednesses holding for pure
states. We identify a class of entangled states that, for fixed marginals, are
globally more mixed than product states when measured by the linear entropy.
Such states cannot be discriminated by the majorization criterion.