  We obtain new information about divisors on the $d-$th symmetric power
$C_{d}$ of a general curve $C$ of genus $g \geq 4.$ This includes a complete
description of the effective cone of $C_{g-1}$ and a partial computation of the
volume function on one of its non-nef subcones, as well as new bounds for the
effective and movable cones of $C_{d}$ in the range $\frac{g+1}{2} \leq d \leq
g-2.$ We also obtain, for each $g \geq 5,$ a divisor on $C_{g-1}$ with
non-equidimensional stable base locus. For a general hyperelliptic curve $C$ of
genus $g,$ we obtain a complete description of the effective cone of $C_{d}$
for $2 \leq d \leq g$ and an integral divisor on $C_{g-1}$ which has
non-integral volume whenever $g$ is not a power of 2.
