  Quantifying entanglement in composite systems is a fundamental challenge, yet
exact results are only available in few special cases. This is because hard
optimization problems are routinely involved, such as finding the convex
decomposition of a mixed state with the minimal average pure-state
entanglement, the so-called convex roof. We show that under certain conditions
such a problem becomes trivial. Precisely, we prove by a geometric argument
that polynomial entanglement measures of degree 2 are independent of the choice
of pure-state decomposition of a mixed state, when the latter has only one pure
unentangled state in its range. This allows for the analytical evaluation of
convex roof extended entanglement measures in classes of rank-two states
obeying such condition. We give explicit examples for the square root of the
three-tangle in three-qubit states, and show that several representative
classes of four-qubit pure states have marginals that enjoy this property.
