We study the question of the existence of non-mitotic sets in NP. We show under various hypotheses that:

• 1-tt-mitoticity and m-mitoticity differ on NP.
• 1-tt-reducibility and m-reducibility differ on NP.
• There exist non-T-autoreducible sets in NP (by a result from Ambos-Spies, these sets are neither T-mitotic nor m-mitotic).
• T-autoreducibility and T-mitoticity differ on NP (this contrasts the situation in the recursion theoretic setting, where Ladner showed that autoreducibility and mitoticity coincide).
• 2-tt autoreducibility does not imply weak 2-tt-mitoticity.
• 1-tt-complete sets for NP are nonuniformly m-complete.