It is shown that the minimum residual algorithm (MINRES) is able to generate spectral filters sharp enough to obtain bound vibrational eigenstates of NO2 (J = 0) by direct access in the most dense part of the spectrum even for the worst near-degeneracy cases. The same is not true for filters constructed as an expansion of the spectral density operator via Chebyshev polynomials. The best performance is obtained in a progressively restarted scheme in which the sharpness of the filter is increased between subsequent restarts to accompany the refinement of the state. Best efficiency and most convenient handling is obtained with early restarts using the Chebyshev-filter, whereas the MINRES-filter is more efficient later in the filtering procedure, where sharp peaking of the filter action is necessary.