We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the W -class, which only possess globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits that are not convexly balanced as for SL invariant families of entanglement, but only affinely balanced. For these states all possible SL-invariants vanish, hence they are part of the SL null-cone. Instead, they will possess at least a certain unitary invariant.As an interesting byproduct it is demonstrated that the exact convex roof is reached in the ranktwo case of a homogeneous polynomial SL-invariant measure of entanglement of degree 2m, if there is a state which corresponds to a maximally m-fold degenerate solution in the zero-polytope that can be combined with the convexified minimal characteristic curve to give a decomposition of ρ. If more than one such state does exist in the zero polytope, a minimization must be performed. A better lower bound than the lowest convexified characteristic curve is obtained if no decomposition of ρ is obtained in this way.