I consider various possibilities for making gamma-ray bursts, particularly from close binaries. In addition to the much-studied neutron star+neutron star and black hole+neutron star cases usually considered good candidates for short-duration bursts, there are also other possibilities. In particular, neutron star+massive white dwarf has several desirable features. These systems are likely to produce long-duration gamma-ray bursts (GRBs), in some cases definitely without an accompanying supernova, as observed recently. This class of burst would have a strong correlation with star formation and occur close to the host galaxy. However, rare members of the class need not be near star-forming regions and could have any type of host galaxy. Thus, a long-duration burst far from any star-forming region would also be a signature of this class. Estimates based on the existence of a known progenitor suggest that this type of GRB may be quite common, in agreement with the fact that the absence of a supernova can only be established in nearby bursts.