For parametrized families of dynamical systems, two major goals are classifying the systems up to topological conjugacy, and understanding the structure of the bifurcation locus. The family Fλ = z^n + λ/z^d gives a 1-parameter, n+d degree family of rational maps of the Riemann sphere, which arise as singular perturbations of the polynomial z^n. This work presents several results related to these goals for the family Fλ, particularly regarding a structure of "necklaces" in the λ parameter plane. This structure consists of infinitely many simple closed curves which surround the origin, and which contain postcritically finite parameters of two types: superstable parameters and escape time Sierpinski parameters. First, we derive a dynamical invariant to distinguish the conjugacy classes among the superstable parameters on a given necklace, and to count the number of conjugacy classes. Second, we prove the existence of a deeper fractal system of "subnecklaces," wherein the escape time Sierpinski parameters on the previously known necklaces are themselves surrounded by infinitely many necklaces
