  We have made a parametric study of s-process nucleosynthesis in the metal
poor ([Fe/H]=-2.7) stars LP625-44 and LP706-7. We find that a high neutron
exposure and a small overlap factor are necessary to fit the abundance pattern
observed in these two metal-deficient stars, particularly the abundance ratios,
Pb/Ba $\approx 1$ and Ba/Sr $\approx 10$. We have also constructed stellar
models to better understand how such s-process conditions could arise. We have
calculated a 2$M_\odot$ model star with metallicity [Fe/H]=-2.7 from the ZAMS
up to AGB phase. We find that for such low-metallicity stars the He convective
shell reaches the bottom of the overlying H-rich envelope at the second thermal
pulse. Protons are then carried into the hotter He burning layers and $^{13}$C
is formed as protons mix into the He shell. Subsequently, material in the
H-flash driven convective zone experiences a high neutron exposure due to the
$^{13}$C($\alpha$, n) reaction. This results in a new neutron-capture s-process
paradigm in which the abundances are characterized by only one neutron
exposure. We suggest that this new s-process site may be a significant
contributor to the s-process abundances in low-metallicity ([Fe/H] $\le -2.5$)
stars.
