Experience with the current generation of astronomical single laser guide star (LGS) adaptive optics (AO) systems
has demonstrated system performance that is often limited by residual tip-tilt errors induced by the paucity of
bright tip-tilt natural guide stars (NGS). To overcome this limitation, we are developing a new generation of
tip-tilt sensors that will operate at near-infrared wavelengths where the NGS is sharpened to the diffraction limit.
To optimize performance, single LGS AO systems utilizing sharpened tip-tilt NGS should generally not point
their LGS directly toward their science target. Rather, optimal performance for wide sky coverage is obtained by
offsetting LGS pointing along a radius connecting the science target and the tip-tilt NGS. We demonstrate that
determination of the jointly optimized LGS pointing angle and tip-tilt wavefront sensor (WFS) integration time
can improve performance metrics by factors of several, particularly for faintest NGS operation. We find the LGS
offset should be as much as 1/2 the distance to the NGS to maximize Strehl ratio at near-infrared wavelengths
and ≈ 1/4 the distance to the NGS to maximize ensquared energy, with lesser off-pointing for brighter NGS.
Future AO systems may benefit from predictive determination of optimal LGS offsetting, based upon changing
atmospheric conditions and observational geometries.