  On a special line bundle $L$ on a projective curve $C$ we introduce a
geometric condition called $(\Delta_q)$. When $L=K_C$ this condition implies
gon$(C) \ge q+2$. For an arbitrary special $L$ we show that $(\Delta_3)$
implies that $L$ has the well-known property $(M_3)$, generalizing a similar
result proved by Voisin in the case $L=K_C$.
