RNAi is a conserved mechanism in which small RNAs induce silencing of complementary targets. How Argonaute-bound small RNAs are targeted for degradation is not well understood. We show that the adenyl-transferase Cid14, a member of the TRAMP complex, and the uridyl-transferase Cid16 add non-templated nucleotides to Argonaute-bound small RNAs in fission yeast. The tailing of Argonaute-bound small RNAs recruits the 30-50 exonuclease Rrp6 to degrade small RNAs. Failure in degradation of Argonaute-bound small RNAs results in accumulation of 'noise' small RNAs on Argonaute and targeting of diverse euchromatic genes by RNAi. To protect themselves from uncontrolled RNAi, cid14 Delta cells exploit the RNAi machinery and silence genes essential for RNAi itself, which is required for their viability. Our data indicate that surveillance of Argonaute-bound small RNAs by Cid14/Cid16 and the exosome protects the genome from uncontrolled RNAi and reveal a rapid RNAi-based adaptation to stress conditions.