Optical reception antennas (telescopes) must be capable of receiving communications even when the deep-space laser source is at a small solar elongation (appears from Earth to be located within a small angle of the Sun.) Direct sunlight must not be allowed to shine on the primary reflector of an optical reception antenna, because too much light would be scattered into the signal detectors. A conventional sunshade that does not obstruct the antenna aperture would have to be about five times longer than its diameter for reception at a solar elongation of 12 deg. Such a long sunshade is unwieldy, either on the ground or in space. Since a new large-aperture optical reception antenna will probably have a hexagonally segmented primary reflector, a sunshade consisting of closely packed hexagonal tubes is proposed. It will be mounted in alignment with the segmentation to avoid producing any additional geometric obstruction. The tubes will be extended downward toward the primary reflector, until they reach the envelope of the focused beam to the secondary reflector. When the optical reception antenna is ground based, the other ends of the tubes will be trimmed and the antenna will be mounted so that both the sunshade and the antenna will swing within a sphere whose diameter is only six-fifths the diameter of the primary reflector. If the segmentation involves four rings of hexagons around an absent central hexagon, then this sunshade will be useful when the solar elongation is as small as 12 deg. The usefulness can be extended to 10 deg by adding shutters to block the tube corners that admit off-axis sunlight. Vanes or slats may be inserted in the tubes to permit operation at 6 deg, or double vanes down to 3 deg. The structure of the sunshade is very strong and may be used to support the secondary reflector instead of an independent support.