A self-encoding system designed to have strict "compartition" of the molecules, i.e., to contain only a single molecule of DNA in each compartment, was established, and its evolutionary fate was analyzed. The system comprised the Thermus thermophilus DNA polymerase gene as the informational molecule and its protein product replicating the gene as the functional molecule. Imposing strict compartition allows the self-encoding system to last up to at least the tenth generation, whereas the system ceased to work after the third generation when loose compartition initiated with 100 molecules was imposed. These results provide experimental evidence on the importance of compartition for the maintenance of a self-encoding system. In addition, the extent of diversity in self-replication activity of the compartments was found to be another vital difference in the evolutionary dynamics between the strict and loose compartitions. Although the system with strict compartition provides widely diversified activity of the compartments at each generation, the values of the activity diverge only within a small range in the system with loose compartition. When the variety in the activity of a compartment is small, functional selection becomes weak, and to conform Darwinian evolution may become unfeasible. Therefore, strict compartition is essential for the evolvability of a self-encoding system.