  Simulations of the Lebowitz length, $\xi_{\text{L}}(T,\rho)$, are reported
for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte
for densi ties $\rho\lesssim 4\rho_c$ and $T_c \lesssim T \lesssim 40T_c$.
Finite-size eff ects are elucidated for the charge fluctuations in various
subdomains that serve to evaluate $\xi_{\text{L}}$. On extrapolation to the
bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and
Fisher, 1998) are seen to fail badly when $\rho > {1/10}\rho_c$ (with $\rho_c
a^3 \simeq 0.08$). At highe r densities $\xi_{\text{L}}$ rises above the Debye
length, $\xi_{\text{D}} \prop to \sqrt{T/\rho}$, by 10-30% (upto $\rho\simeq
1.3\rho_c$); the variation is portrayed fairly well by generalized
Debye-H\"{u}ckel theory (Lee and Fisher, 19 96). On approaching criticality at
fixed $\rho$ or fixed $T$, $\xi_{\text{L}}(T, \rho)$ remains finite with
$\xi_{\text{L}}^c \simeq 0.30 a \simeq 1.3 \xi_{\text {D}}^c$ but displays a
weak entropy-like singularity.
