Using CGS4 on UKIRT, we have obtained 2.00-2.45 mu m infrared spectra of a number of low-mass X-ray binaries including Sco X-1, Sco X-2 and GX1 3+1. Sco X-1 shows emission lines only, supporting our previous conclusion that the spectral type of the evolved secondary must be earlier than G5. Emission lines are also seen in the spectrum of Sco X-2, confirming the identity of the IR counterpart. We report the detection of CO bands in GX1 3+1, and estimate the most likely spectral type of the secondary to be K5III. We also find P Cygni-type profiles in the Brackett gamma lines of Sco X-1 and GX1 3+1, indicating the presence of high-velocity outflows in these systems. We present spectra of candidate IR counterparts to several other elusive X-ray binaries. Finally, implications for the nature and classification of these systems are discussed.