We consider a 6-dimensional spacetime which is periodic in one of the extra dimensions and compact in the other. The periodic direction is defined by two 4-brane boundaries. Both static and nonstatic exact solutions, in which the internal spacetime has a constant radius of curvature, are derived. In the case of static solutions, the brane tensions must be tuned as in the 5-dimensional Randall-Sundrum model; however, no additional fine-tuning is necessary between the brane tensions and the bulk cosmological constant. By further relaxing the sole fine-tuning of the model, we derive nonstatic solutions, describing de Sitter or anti-de Sitter 4-dimensional spacetimes, that allow for the fixing of the interbrane distance and the accommodation of pairs of positivenegative and positive-positive tension branes. Finally, we consider the stability of the radion field in these configurations by employing small, time-dependent perturbations around the background solutions. In analogy with results drawn in five dimensions, the solutions describing a de Sitter 4-dimensional spacetime turn out to be unstable while those describing an anti-de Sitter geometry are shown to be stable.