A previous study on B12N12 showed that the Hartree-Fock (HF) method, local density approximation (LDA), and gradient-corrected density functional theory (specifically B3LYP) all agree in predicting that the cage isomer of B12N12 is the most stable. If the cage is the most stable (BN)(x) for x = 12, then the energetic crossover between rings and cages must take place at some x < 12. Rings would be most stable for small molecules, and cages would be most stable for larger molecules. The current study explores the question of whether rings or cages are more stable at sizes smaller than B12N12, With the goal of defining a crossover point between rings and cages. These issues are examined by theoretical calculations using the HF, LDA, and B3LYP methods, along with second-order perturbation theory (MP2). In particular, an energetic comparison is carried out between the ring and cage isomers of (BN)(x) for x = 8-11. The major result is that boron nitride cages are more stable than rings if at least two of the six four-membered rings an isolated by hexagons, an arrangement that is first seen for the B11N11 cage.