Close binaries are widely believed to exist in large numbers in the cores of globular clusters. If present, these binaries are critical sources and sinks of energy that drive the dynamical evolution of their host clusters. I report on HST searches for binaries (based on variability) in the outskirts and cores of several globular clusters; dwarf novae should be particularly easy to find. Dense and loose clusters have been thoroughly searched on timescales ranging from minutes to years. Detailed simulations demonstrate that virtually all binaries with M < 8, amplitudes > 0.1 mag and periods of 2–20 hours should have been found. This includes virtually all known contact binaries. At least 1/3 of all dwarf novae present in several globulars should also have been seen (very easily!) in eruption at M = 4 − 6.
Simple tidal capture theory predicts that dozens of interacting binaries should have been found in our searches; the observed number is typically one or two objects per cluster. Unless tidal capture cataclysmic binaries are rapidly destroyed, ejected, or much fainter than most of their Galactic counterparts, we must conclude that very close binaries in globular cores are rare, and that their total influence on cluster dynamical evolution is less than currently claimed.