There are several exceptions to both the Exclusionary Rule and the fruit of the poisonous tree doctrine:

Independent Source Doctrine: Evidence discovered in part from an independent, untainted source. [Murray v. United States, (1988)]

Inevitable Discovery Rule: the evidence would have been found despite the unconstitutional action. [Nix v. William, (1984)]

Attenuated Connection Principle: The chain of cause and effect is too attenuated to tie directly to the unconstitutional action. [Wong Sun v. United States, (1963)]

Good Faith Rule: A search warrant not based on probable cause was issued, but acted upon in good faith by government agents. [US v. Leon, (1984).]