We consider a thick polymer model with the purpose of providing a coarse-grained description for double-stranded DNA (dsDNA). The model is used to gain insight into how the intrinsic thickness of DNA affects the behaviour of the biomolecule subject to compaction. Our reference system is provided by the process of DNA packaging inside a viral capsid that has been recently characterized through delicate single-molecule experiments. The simplest of the two models considered here is able to provide a satisfactory quantitative accord with experimental measurement by using, as only inputs, the known dsDNA diameter and the base-pair spacing. In a second model we further incorporate a standard bending rigidity term obtaining a better agreement with experiments.