<p>The paper deals with bounds for Krylov methods which are insensitive in low rank perturbations. In finite dimensional cases resolvents are meromorphic in the whole plane and robust bounds have been constructed using special growth functions created for operator valued meromorphic functions. In this paper such bounds are derived without use of those special tools. In particular, convergence in generic hermitean problems and highly non-normal problems are effectively analysed with the same technique based on representing the resolvent using <i>spectral polynomials</i> and thus for example the conditioning of eigenvector bases does not show up at all.</p>