Self-renewing tissues require that a constant number of proliferating cells is maintained over time. This maintenance can be ensured at the single-cell level or the population level. Maintenance at the population level leads to fluctuations in the number of proliferating cells over time. Often, it is assumed that those fluctuations can be reduced by increasing the number of asymmetric divisions, i.e., divisions where only one of the daughter cells remains proliferative. Here, we study a model of cell proliferation that incorporates a stem-cell niche of fixed size, and explicitly model the cells inside and outside the niche. We find that in this model, fluctuations are minimized when the difference in growth rate between the niche and the rest of the tissue is maximized and all divisions are symmetric divisions, producing either two proliferating or two nonproliferating daughters. We show that this optimal state leaves visible signatures in clone size distributions and could thus be detected experimentally.