We propose and analyze a new modulation sequence for Random- Modulation Continuous-Wave (RM-CW) lidar. It is compared to known sequences, and shown to have significantly better, and nearly-ideal, signal properties. Namely, the cross- correlation function of this new sequence - named the AA1- sequence - consists of single peaks separated by zeros. Consequently, unlike the A1- and A2-sequence, it is immune to interference caused by backscattering from different ranges. Also, since the demodulation sequence is balanced, the new sequence, unlike the M-sequence, does not require the low laser output power to be zero to maintain desired cross-correlation properties; in lidar using a semiconductor laser as a transmitter, this would eliminate coupling between the demodulated signal amplitude and the emission wavelength, and thus facilitate wavelength-dependent measurements. Furthermore, we have calculated the post- demodulation signal-to-noise ratio in the presence of an additive noise of arbitrary power spectra density - it is applicable in all cases where the noise does not depend on the signal, which is typical in direct-detection mid-IR lidar. The results show that in baseband transmission all these sequences have similar noise properties, except that the M-sequence - due to its imbalance property - has a much stronger near-zero-frequency noise pickup, which results in significantly worse noise performance in practical systems. Therefore, we claim that the new modulation sequence would yield superior performance in RM-CW lidar.