  We compare the behavior of different lattice Dirac operators in gauge
backgrounds which are lattice discretizations of a classical instanton. In
particular we analyze the standard Wilson operator, a chirally improved Dirac
operator and the overlap operators constructed from these two operators. We
discuss the flow of real eigenvalues as a function of the instanton size. An
analysis of the eigenvectors shows that overlap fermions with the Wilson
operator as input operator have difficulties with reproducing the continuum
zero mode already for moderately small instantons. This problem is greatly
reduced when using the chirally improved operator for the overlap projection.
