The differences between observed solar p-mode frequencies and the frequencies of a reference model can be inverted to infer the structure of the Sun using a variety of linear inversion techniques. However, it is well known that the adiabatic description, which is often employed in frequency calculations, breaks down in the outermost layers of the Sun. This and other uncertainties in the treatment of the superficial layers introduce a slowly varying frequency-dependent function into the frequency differences. We present here a technique to pre-process the frequency differences prior to applying any of the standard inversion techniques in order to eliminate the frequency dependent component which arises from the near-surface uncertainties, suppressing also the corresponding contributions from the kernels relating frequency differences to differences in structure. This is achieved by applying suitable linear filters to the frequency differences and to the mode kernels. We obtain the filtered kernels and demonstrate that the surface contribution can be successfully suppressed. We also present the results of the inversions performed after the data and mode kernels have been filtered.