Comparative genomics has revealed that some species have exceptional genomes, compared to their closest relatives. For instance, some species have undergone a strong reduction of their genome with a drastic reduction of their genic repertoire. Deciphering the causes of these atypical trajectories can be very difficult because of the many phenomena that are intertwined during their evolution (e.g. changes of population size, environment structure and dynamics, selection strength, mutation rates...). Here we propose a methodology based on synthetic experiments to test the individual effect of these phenomena on a population of simulated organisms. We developed an evolutionary model - aevol - in which evolutionary conditions can be changed one at a time to test their effects on genome size and organization (e.g. coding ratio). To illustrate the proposed approach, we used aevol to test the effects of a strong reduction in the selection strength on a population of (simulated) bacteria. Our results show that this reduction of selection strength leads to a genome reduction of ~35% with a slight loss of coding sequences (~15% of the genes are lost - mainly those for which the contribution to fitness is the lowest). More surprisingly, under a low selection strength, genomes undergo a strong reduction of the noncoding compartment (~55% of the noncoding sequences being lost). These results are consistent with what is observed in reduced Prochlorococcus strains (marine cyanobacteria) when compared to close relatives.