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The use of spectral shaping constrained codes is commonplace in baseband digital communication systems. In this study, the authors consider the use of constrained codes in bandpass systems through the design of DC-free codes for the complex baseband representations of commonly used signalling constellations including quaternary phase shift keying, eight-phase shift keying and sixteen quadrature amplitude modulation. The authors construct DC-free codes for these signalling alphabets and present their spectral performance. They show that, similar to DC-free codes for baseband systems, the variance of the running digital sum remains a good indicator of spectral performance and that Justesen's relationship between the sum variance and cut-off frequency holds.