We present near-infrared (NIR) imaging observations of three transient neutron star X-ray binaries, SAX J1753.5-2349, SAX J1806.5-2215 and AX J1754.2-2754. All three sources are members of the class of `very faint X-ray transients which exhibit X-ray luminosities $L_Xlesssim10^{36}$ erg s$^{-1}$. The nature of this class of sources is still poorly understood. We detect NIR counterparts for all three systems and perform multi-band photometry for both SAX J1753.5-2349 and SAX J1806.5-2215, including narrow-band Br$_{gamma}$ photometry for SAX J1806.5-2215. We find that SAX J1753.5-2349 is significantly redder than the field population, indicating that there may be absorption intrinsic to the system, or perhaps a jet is contributing to the infrared emission. SAX J1806.5-2215 appears to exhibit absorption in Br$_{gamma}$, providing evidence for hydrogen in the system. Our observations of AX J1754.2--2754 represent the first detection of a NIR counterpart for this system. We find that none of the measured magnitudes are consistent with the expected quiescent magnitudes of these systems. Assuming that the infrared radiation is dominated by either the disc or the companion star, the observed magnitudes argue against an ultracompact nature for all three systems.
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