Heterostructures including the members of the 6.1{AA} semiconductor family (AlSb, GaSb, and InAs) are used in infrared optoelectronic devices as well as a variety of other applications. Short-period superlattices of these materials are also of interest for creating composite materials with designer infrared dielectric functions. The conditions needed to create sharp InAs/GaSb and InAs/AlSb interfaces are well known, but the AlSb/GaSb interface is much less well-understood. In this article, we test a variety of interventions designed to improve interface sharpness in AlSb/GaSb short-period superlattices. These interventions include substrate temperature, III:Sb flux ratio, and the use of a bismuth surfactant. Superlattices are characterized by high-resolution x-ray diffraction and infrared spectroscopy. We find that AlSb/GaSb short-period superlattices have a wide growth window over which sharp interfaces can be obtained.