We report on the experimental test of a new concept for reducing the limitation on short-term frequency stability of passive frequency standards due to local oscillator phase noise. This concept is general and can be applied to many passive frequency standards. Systems that use sinewave modulation to interrogate a stable resonance are limited in short-term frequency stability by phase noise at the second harmonic of the modulation, f(m). This effect limits the fractional frequency stability to approximately sigma(y)(tau) = 0.9(f(m)/nu0) (S(phi)(2f(m)))1/2tau-1/2, where nu0 is the carrier frequency and S(phi)(2f(m)) is the phase noise at twice the modulation frequency. (Contributions from higher even harmonics of the modulation generally can be neglected). This new concept uses notch filters at +/-2f(m) from the carrier to reduce this effect. Tests on a modified passive rubidium standard demonstrate an improvement of approximately 18 in sigma(y)(tau). The dual notch filters proved to be feasible and were obtained commercially. Measurements suggest that ultimate performances of less than 2 x 10(-14)tau-1/2 are possible if the atomic resonance has sufficient quality.