  We study cutoff effects at tree-level of perturbation theory for maximally
twisted mass Wilson, overlap and the recently proposed Creutz fermions. We
demonstrate that all three kind of lattice fermions exhibit the expected O(a^2)
scaling behaviour in the lattice spacing. In addition, the sizes of these
cutoff effects are comparable for the three kinds of lattice fermions
considered here. Furthermore, we analyze situations when twisted mass fermions
are not exactly at maximal twist and when overlap fermions are studied in
comparison to twisted mass fermions when the quark masses are not matched.
