1. Strategic -- The world is going to die nukes. These are big nukes on ICBMs. If the opponent launches a strategic nuke, you launch all of yours and kill them too.
2. Tactical -- Small nukes that you shoot at the opponent's army before sending in your troops.
You're thinking of strategic nukes. But strategic nukes are far weaker if you have a dirty explosion: its probably better to have a more complete bomb. Tactical nukes absolutely must be clean, because your own troops are in the area.
Strategic nukes are typically fission-fusion-fission devices with both more yield and more fallout than a cleaner fission-fusion design of the same weight.
