Genome packing in adenovirus has long evaded precise description, since the viral dsDNA molecule condensed by proteins (core) lacks icosahedral order characteristic of the virus protein coating (capsid). We show that useful insights regarding the organization of the core can be inferred from the analysis of spatial distributions of the DNA and condensing protein units (adenosomes). These were obtained from the inspection of cryo-electron tomography reconstructions of individual human adenovirus particles. Our analysis shows that the core lacks symmetry and strict order, yet the adenosome distribution is not entirely random. The features of the distribution can be explained by modeling the condensing proteins and the part of the genome in each adenosome as very soft spheres, interacting repulsively with each other and with the capsid, producing a minimum outward pressure of ∼0.06 atm. Although the condensing proteins are connected by DNA in disrupted virion cores, in our models a backbone of DNA linking the adenosomes is not required to explain the experimental results in the confined state. In conclusion, the interior of an adenovirus infectious particle is a strongly confined and dense phase of soft particles (adenosomes) without a strictly defined DNA backbone.