We report on a detailed study of the spectral and temporal properties of the neutron star low-mass X-ray binary SLX 1737-282, which is located only ∼1° away from Sgr A*. The system is expected to have a short orbital period, even within the ultracompact regime, given its persistent nature at low X-ray luminosities and the long duration thermonuclear burst that it has displayed. We have analysed a Suzaku (18 ks) observation and an XMM-Newton (39 ks) observation taken 7 yr apart. We infer (0.5-10 keV) X-ray luminosities in the range of 3-6 × 1035ergs-1, in agreement with previous findings. The spectra are well described by a relatively cool (kTbb = 0.5 keV) blackbody component plus a Comptonized emission component with Γ ∼ 1.5-1.7. These values are consistent with the source being in a faint hard state, as confirmed by the ∼20 per cent fractional root-mean-square amplitude of the fast variability (0.1-7 Hz) inferred from the XMM-Newton data. The electron temperature of the corona is ≳7 keV for the Suzaku observation, but it is measured to be as low as ∼2 keV in the XMM-Newton data at higher flux. The latter is significantly lower than expected for systems in the hard state. We searched for X-ray pulsations and imposed an upper limit to their semi-amplitude of 2 per cent (0.001-7 Hz). Finally, we investigated the origin of the low-frequency variability emission present in the XMM-Newton data and ruled out an absorption dip origin. This constraint the orbital inclination of the system to ≲65° unless the orbital period is longer than 11 h (i.e. the length of the XMM-Newton observation).