A method for transmitting covertly employs three features in a novel combination to create a transmission waveform that has no detectable artifacts. First, the method employs spread spectrum, such as a direct sequence spread spectrum signal, to transmit the power level below the noise floor. Second, the method modulates the phase of each chip in the spread spectrum signal using a chaotic sequence. Third, the method filters the transmission signal using a pulse shaped filter to depress blind detection features in the amplitude modulation and higher order power spectral densities. The novel combination of these features results in a practically invisible and undetectable transmission waveform. Many other features are disclosed herein to optimize this combination.