Hollow-core fibers with a single ring of circular anti-resonant tubes as the cladding provide a simple way of getting a negative-curvature hollow-core, resulting in broadband low-loss transmission with little power overlap in the glass. These fibers show a significant improvement in loss performance if the anti-resonant tubes have nested tubes inside them, and here we investigate the role of the shape and position of these nested elements. By allowing the circular nested elements to become semi-circular we selectively change the position or curvature of the nested elements. We find that the loss performance is quite insensitive to the curvature of the nested element, while the distance from the core boundary to the outer perimeter of the nested element is much more critical. Interestingly, the additional freedom of the semi-circular nested elements allows optimizing them for a better loss performance than the ideal full-circle design.