In [V. Galdi et al., Phys. Rev. E 57, 6470 (1998)] a thorough characterization in terms of receiver operating characteristics of stochastic-resonance detectors of weak harmonic signals of known frequency in additive Gaussian noise was given. It was shown that strobed sign-counting based strategies can be used to achieve a nice trade-off between performance and cost, by comparison with noncoherent correlators. Here we discuss the more realistic case where besides the sought signal (whose frequency is assumed known) further unwanted spectrally nearby signals with comparable amplitude are present. Rejection properties are discussed in terms of suitably defined false-alarm and false-dismissal probabilities for various values of interfering signal(s) strength and spectral separation.