The Ginga hard X-ray spectrum of EF Eri is well fitted by a single-temperature Raymond-Smith spectrum with kT similar to 14 keV with reduced iron abundance, together with its reflection from the white dwarf surface. However, calculations of the shock structure indicate that the X-ray emission should consist of multitemperature components as the gas cools and settles on to the photosphere. We fit approximate models of such continua, together with their reflection, and find that, while these are not required by the data, they give as good a description of the spectrum as the single-temperature models. The maximum temperature material is derived to be at similar to 25 keV, close to that predicted by strong shock models, but even with these more realistic models the data still require that iron is a factor similar to 2 below solar abundance. Radiation transfer in the hot shock is shown to be important, as the emission region is expected to be optically thick in the iron K alpha resonance lines, whilst remaining optically thin in the continuum. However, this is unlikely to be the cause of the low observed line equivalent width as there is no viable alternative decay path for the Lyman alpha line in H- and He-like iron. The 6.4-keV iron line from fluorescence from the reflector is also smaller than expected by a factor similar to 2, making a true underabundance of iron in this system the most likely explanation. We also calculate the absorption expected from the pre-shock material in the limit where the dense streams of material raining on to the surface to produce the soft X-rays are dominant. The expected phase dependence of this absorption does not match well to that seen in EF Eri, but this may be due to non-circular or multiple accretion sites or photoionization of the pre-shock column.