The analysis of a coronal loop observed by CDS and EIT on board SOHO is presented. The loop was situated above the North-East limb at a latitude of ~48°, being clearly visible in the hottest lines of the dataset, Fe xvi 360.76 Å, i.e. greater than 2 000 000 K. The cooler lines in the sample (i.e. O v 629.73 Å and He i 584.35 Å) showed only a brightening at the footpoints location. Based on the Fe xiv 353.84/334.17 line ratio, the electron density along the loop was determined following three different approaches for the background subtraction. No differences, within the error bars, can be found between the three methods. At the apex, the density is 0.9×109 cm-3, while at the footpoint it is 50% greater, i.e. 1.4×109 cm-3. The inferred filling factor values along the loop, at the formation temperature of the lines, are in the range 0.2-0.9. One dimensional hydrodynamic modelling of the loop along a given field line, gravity neglected, was performed. A minimum χ2 analysis results in a best fit case where the total energy input is directed preferentially to the loop footpoint (the heating rate is three times larger at the base than at the apex). An isochoric solution can not be ruled out completely. The exercise illustrates the necessity of accurate spectral diagnostics in order to derive definite conclusions from theoretical models and suggests the need for simultaneous density and temperature diagnostics.