It has been shown that certain static nonlinearities that display stochastic resonant behaviour can be used as Signal-to-Noise Ratio amplifiers for a sinusoidal signal corrupted by noise, and that such nonlinearities can serve as pre-processors for further linear processing. We demonstrate that by swapping the roles of pre-processor and processor, i.e. by using a linear filter as a pre-processor for the nonlinearity, the resonant character of the curves is preserved, but with significant improvements of SNR gain. This is demonstrated on nonlinearities otherwise incapable of producing SNR gain greater than unity.