  We propose a correlated spin-singlet-pairs wave function to describe the
spin-gap phase of the one-dimensional $t-J$ model at low density. Adding a
Jastrow factor with a variational parameter, $\nu$, first introduced by
Hellberg and Mele, is shown to correctly describe the long-range behavior
expected for the Luther-Emery phase. Using the variational Monte Carlo method
we establish a relation between $\nu$ and the Luttinger exponent $K_\rho$,
$K_\rho=\frac{1}{2\nu}$.
