  We show that every rank one smooth Fano threefold has a weak Landau-Ginzburg
model coming from a toric degeneration. The fibers of these Landau-Ginzburg
models can be compactified to K3 surfaces with Picard lattice of rank 19. We
also show that any smooth Fano variety of arbitrary dimension which is a
complete intersection of Cartier divisors in weighted projective space has a
very weak Landau-Ginzburg model coming from a toric degeneration.
