A previous paper (Unsal, E.; Mason, G.; Ruth, D. W.; Morrow, N. R. J. Colloid Interface Sci. 2007,315,200-209) reported experiments involving counter-current spontaneous imbibition into a model pore system consisting of a rod in an angled slot covered by a glass plate. Such an arrangement gives two tubes with different cross-sections (both size and shape) with an interconnection through the gap between the rod and the plate. In the previous experiments, the wetting phase advanced in the small tube and nonwetting phase retreated in the large tube. No bubbles were formed. In this paper, we study experimentally and theoretically the formation of bubbles at the open end of the large tube and their subsequent snap-off. Such bubbles reduce the capillary back pressure produced by the larger tube and can thus have an effect on the local rate of imbibition. In the model pore system, the rod was either in contact with the glass, forming two independent tubes, or the rod was spaced from the glass to allow cross-flow between the tubes. For small gaps, there were three distinct menisci. The one with the highest curvature was between the rod and the plate. The next most highly curved was in the smaller tube, and the least highly curved meniscus was in the large tube and this was the tube from which the bubbles developed. The pressure in the dead end of the system was recorded during imbibition. Once the bubble starts to form outside of the tube, the pressure drops rapidly and then steadies. After the bubble snaps off, the pressure rises to almost the initial value and stays essentially constant until the next bubble starts to form. After snap-off, the meniscus in the large tube appears to invade the large tube for some distance. The snap-off is the result of capillary instability; it takes place significantly inside the large tube with flow of wetting phase moving in the angular corners. As imbibition into the small tube progresses, the rate of imbibition decreases and the time taken for each bubble to form increases, slightly increasing the pressure at which snap-off occurs. The snap-off curvature is only about two-thirds of the curvature of a theoretical cylindrical meniscus within the large tube and about 40% of the curvature of the actual meniscus spanning the large tube.