  We consider spectral quantities in lattice QCD and determine the asymptotic
behavior of their discretization errors. Wilson fermion with
O$(a)$-improvement, (M\"obius) Domain wall fermion (DWF), and overlap Dirac
operators are considered in combination with the commonly used gauge actions.
Wilson fermions and DWF with domain wall height $M_5=1+{\rm O}(g_0^2)$ have the
same, approximate, form of the asymptotic cutoff effects: $ K\,a^2\left[\bar
g^2(a^{-1})\right]^{0.760}$. A domain wall height $M_5=1.8$, as often used,
introduces large mass-dependent $K'(m)\,a^2\left[\bar
g^2(a^{-1})\right]^{0.518}$ effects. Massless twisted mass fermions have the
same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is
included. For their mass-dependent cutoff effects we have information on the
exponents $\hat\Gamma_i$ of $\bar g^2(a^{-1})$ but not for the pre-factors. For
staggered fermions there is only partial information on the exponents.
  We propose that tree-level ${\rm O}(a^2)$ improvement, which is easy to do
[2], should be used in the future -- both for the fermion and the gauge action.
It improves the asymptotic behavior in all cases.
