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The radioactivity produced by a nuclear explosion comes chiefly from two sources: 1) fission products (fragments of plutonium or uranium atoms) and 2) free neutrons, which enter atoms of many common elements and make them radioactive. It does not seem likely that much can be done to reduce the total quantity of the fission products. But bomb physicists may have learned how to make the explosion produce fission products that are less radioactive, or that lose their activity before the fallout reaches the ground.
It is more likely that something has been done to control the bomb's free neutrons. One device would be to make sure that the bomb's casing and mechanism do not contain material that is made radioactive by neutrons. Another would be to provide material that soaks up neutrons without becoming dangerously radioactive itself.
A third possibility is that "clean" H-bombs may not rely on fission at all. The mighty bomb of 1954, although involving a fusion (hydrogen) reaction of some sort, got most of its energy from fissioning uranium, and therefore produced a gigantic amount of fission products. The latest models may be designed to use only a little fissioning uranium for a detonator, and to get the bulk of their energy from a fusion reaction whose end product is a stable element such as helium. In that case they need produce hardly any fallout. "Clean" H-bombs may be unusually expensive, and not necessarily ideal in the case of an all-out nuclear war. A good strong fallout enables a few explosions to put a whole nation out of action, and is therefore a military weapon too valuable to ignore. Fallout can be maximized as well as minimized, and more easily. Presumably, the AEC has given at least theoretical attention to this possibility too.