  One of the main challenges in simulations on Lefschetz thimbles is the
computation of the relative weights of contributing thimbles. In this paper we
propose a solution to that problem by means of computing those weights using a
reweighting procedure. Besides we present recipes for finding parametrizations
of thimbles and anti-thimbles for a given theory. Moreover, we study some
approaches to combine the Lefschetz thimble method with the Complex Langevin
evolution. Our numerical investigations are carried out by using toy models
among which we consider a one-site z^4 model as well as a U(1) one-link model.
