Abstract. The differential emission measure (DEM) of a solar active region is derived from SERTS-89 rocket data between 170 and 450Å . The integral inversion to infer the DEM distribution from spectral line intensities is performed by the data adaptive smoothing approach (Thompson 1990(Thompson , 1991. Our analysis takes into account the density dependence of both ionisation fractions and excitation coefficients according to the collisional-radiative theory as implemented in ADAS, the Atomic Data and Analysis Structure (McWhirter & Summers 1984;Summers 1994;Summers 2001). Our strategy aims at checking, using observational data, the validity and limitations of the DEM method used for analysing solar EUV spectra. We investigate what information it is possible to extract, within defined limitations, and how the method can assist in a number of cases, e.g. abundance determination, spectral line identification, intensity predictions, and validation of atomic cross-sections. Using the above data and theory, it is shown that a spurious multiple peak in the DEM distribution between log(Te) = 6.1 and 6.7, where Te is the electron temperature, may derive from an inaccurate treatment of the population densities of the excited levels and ionisation fractions or from using an integral inversion technique with arbitrary smoothing. Therefore, complex DEM structures, like those proposed for solar and stellar coronae by several authors, must be considered with caution. We address also the issue of systematic differences between iso-electronic sequences and show that these cannot be unambiguously detected in the coronal lines observed by SERTS. Our results indicate that a substantial improvement is required in the atomic modelling of the complex element Fe. The elemental abundance ratio Si/Ne is found to be close to its photospheric value. The same result may be true for the Fe/Ne abundance, but this latter result is uncertain because of the problems found with Fe.