  We give a topological description of the space of quadratic rational maps
with superattractive two-cycles: its "non-escape locus" M2 (the analog of the
Mandelbrot set M) is locally connected, it is the continuous image of M under a
canonical map, and it can be described as M (minus the 1/2-limb), mated with
the lamination of the basilica. The latter statement is a refined version of a
conjecture of Ben Wittner, which in its original version requires local
connectivity of M to even be stated. Our methods of mating with a lamination
also apply to dynamical matings of certain non-locally connected Julia sets.
