  We suggest the procedure that constructs a log Calabi--Yau compactification
of weak Landau--Ginzburg model of a Fano variety. We apply the suggestion for
del Pezzo surfaces and coverings of projective spaces of index one. We also
prove in these cases conjectures relating numbers of components of the fiber
over infinity and of finite fibers with the dimension of an anticanonical
system of the Fano variety and its first nontrivial middle Hodge number,
respectively.
