We outline an approach to physical-layer steganography where the transmitted low-power stego messages are statistically indistinguishable from the Gaussian component of the channel noise (e.g. the thermal noise) observed in the same spectral band, and thus the channel noise itself serves as an effective cover signal. We also demonstrate how the apparent spectral and temporal properties of transmitted additional, higher-power cover signals (including those using the existing communication protocols) can be made to match those of the low-power stego payload and the Gaussian noise, providing extra layers of obfuscation for both the cover and the stego messages. We further illustrate how a specific combination of linear and nonlinear filtering can be used for effective separation of the cover, payload, and/or "friendly jamming" signals even when all transmissions have essentially the same spectral characteristics as well as temporal and amplitude structures, and when there are no explicit differences in the spectral and/or temporal allocations for the cover and the stego messages.