It seems like we could establish some hierarchy (in fact, we already have one implicit in maximum or minimum sentence lengths, though I don't know if that is the right one to use). When an officer asks to engage in a search, he can then state "I am investigating X, we will ignore anything less serious."

If something is seen, it seems like it would be hard to prevent the officer from making a mental note to look into that guy later. We could grant immunity, but that could also get weird. I think just narrowly excluding the evidence uncovered in the search would still probably be an improvement, though (probably...).