The fusion of two black holes --- a signature phenomenon of General Relativity --- is usually regarded as a process so complex that nothing short of a supercomputer simulation can accurately capture it. But this is not quite so – not always. I will explain how the event horizon of the fusion can be found in a very simple way when one of the black holes is much smaller than the other. The construction is not only simple but also accurate, general, and realistic: these fusions are occurring out there, all the time. Remarkably, the ideas and techniques involved are elementary, so the construction can be understood with only a basic knowledge of General Relativity.