  We introduce deformation theoretic methods for determining when a curve $X$
in a non-hyperelliptic jacobian $JC$ will deform with $JC$ to a non-jacobian.
We apply these methods to a particular class of curves in the second symmetric
power $C^{(2)}$ of $C$. More precisely, given a pencil $g^1_d$ of degree $d$ on
$C$, let $X$ be the curve parametrizing pairs of points in divisors of $g^1_d$
(see the paper for the precise scheme-theoretical definition). We prove that if
$X$ deforms infinitesimally out of the jacobian locus with $JC$ then either
$d=4$ or $d=5$, dim$H^0 (g^1_5) = 3$ and $C$ has genus 4.
