Three EXOSAT observations of the low-mass X-ray binary XB1916–053 have revealed extreme variability in the appearance of the dips, ranging from complete absence to two broad, deep dips per 50-min cycle. These dips are believed to result from the obscuration of the central X-ray source by azimuthal structure in the accretion disc; the data suggest that the dips, and thus the disc structure, evolve on a time-scale of hours. The absence of eclipses constrains the orbital inclination of the system to be |$i\lt{79}^{^{\circ}}$|, thus requiring the vertical angular extent of the disc structure to be |$\gt{11}^{^{\circ}}$|. The X-ray spectrum during quiescent (i.e. non-dipping, non-bursting) intervals is well described by a simple power-law model with photon index –1.8. Intensity-selected spectra are well fitted by either a simple power law which becomes flatter with decreasing flux, or a composite model with contributions from a heavily-absorbed component and a non-absorbed, probably Thomson scattered component. Adopting the latter interpretation, we find that the decrease in observed flux during dips can be explained by a decrease in the normalization of the non-absorbed component by a factor of 10, and an increase in the column of the absorbed component from the quiescent value of |$2\times {10}^{21}\text{cm}^{-2}$| (consistent with galactic absorption along the line-of-sight) to a maximum of |$7\times {10}^{23}\text{cm}^{-2}$|. The analysis suggests that the material responsible for the dips is marginally under-abundant in metals by a factor of 3±2 (90 per cent confidence) compared to solar values, assuming that there is no photoionization of this material. From an analysis of four bursts observed from XB1916–053, and the assumption that the peak luminosity in the bursts can be equated with the Eddington luminosity, we derive a distance of 8.4 kpc to the source assuming cosmic abundances, or 10.8 kpc if the accreted material is extremely hydrogen-deficient, as required by published evolutionary models.