  Thurston parameterized quadratic invariant laminations with a non-invariant
lamination, the quotient of which yields a combinatorial model for the
Mandelbrot set. As a step toward generalizing this construction to cubic
polynomials, we consider slices of the family of cubic invariant laminations
defined by a fixed critical leaf with non-periodic endpoints. We parameterize
each slice by a lamination just as in the quadratic case, relying on the
techniques of smart criticality previously developed by the authors.
