  In this paper we investigate two different entanglement measures in the case
of mixed states of two qubits. We prove that the negativity of a state can
never exceed its concurrence and is always larger then
$\sqrt{(1-C)^2+C^2}-(1-C)$ where $C$ is the concurrence of the state.
Furthermore we derive an explicit expression for the states for which the upper
or lower bound is satisfied. Finally we show that similar results hold if the
relative entropy of entanglement and the entanglement of formation are
compared.
