The problem of a constant modulus (CM) continuous wave (CW) waveform design with the thumb-tack ambiguity function that meets the NTIA RSEC requirements is addressed. The ad-hoc and alternating projection techniques are proposed to modify the spectrum of a prototype waveform to meet the NTIA RSEC requirements, retaining the "thumb-tack" property of the original waveform ambiguity function. Periodic binary frequency shift keying (BFSK), Costas FSK, and noise-like waveforms are modified to meet CM and NTIA RSEC requirements. Introduced examples demonstrate the spectrum modification consequences and the proposed technique's efficiency for generating the CM spectrum-controlled waveforms with the thumb-tack ambiguity function.