What exactly is the type of modulation in the DSSS?
the amount of "power" contained in a broad bandwith can "appear" to be different when viewed on a spectrum analyzer set to a narrow resolution bandwidth. For instance, FSK is a contant envelope signal and can appear to be bigger than QAM if captured in a small resolution bandwith. therefore the 2nd/3rd harmonic will also appear to be bigger than that caused by QAM.
Also, the 2nd harmonic is at twice the frequency, so its power/hz will drop by 3 dB, and more so with the 3rd harmonic.