We study mechanisms that operate in interdependent values environments. We show that when defined on knit and strict environments, only constant mechanisms can be ex post incentive compatible. Knitness is also necessary for this result to hold for mechanisms with two alternatives in the range. For partially knit and strict environments, we prove that ex post incentive compatibility extends to groups, and that strategy-proofness implies strong group strategy-proofness in the special case of private values. The results extend to mechanisms operating on non-strict domains under an additional requirement of respectfulness. We discuss examples of environments where our theorems apply