  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 $L_X\lesssim10^{36}$ 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.
