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Using a new quenching technique to minimize gravitationally induced density gradients, we find that the shape $\frac{({\ensuremath{\rho}}_{L}\ensuremath{-}{\ensuremath{\rho}}_{V})}{{\ensuremath{\rho}}_{c}}$ of the xenon liquid-vapor coexistence curve is described over the reduced-temperature range $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}&lt;\ensuremath{\epsilon}&lt;3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ [where $\ensuremath{\epsilon}=\frac{({T}_{c}\ensuremath{-}T)}{{T}_{c}}$] by the pure power law $B{\ensuremath{\epsilon}}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}=0.317\ifmmode\pm\else\textpm\fi{}0.011$. For $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}&lt;\ensuremath{\epsilon}&lt;2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ where $B{\ensuremath{\epsilon}}^{\ensuremath{\beta}}$ is a poor description of our data, adding the first correction term ${B}_{1}{\ensuremath{\epsilon}}^{{\ensuremath{\beta}}_{1}}$ provides an improved description with $\ensuremath{\beta}=0.305\ifmmode\pm\else\textpm\fi{}0.010$ and ${\ensuremath{\beta}}_{1}=0.77\ifmmode\pm\else\textpm\fi{}0.13$ in agreement with lattice-gas, binary-alloy, and $n=1$ magnetic results.