The paper considers the idea of reducing near-Earth space debris by discarding expended stages into the Earth’s atmosphere. The problem of optimizing the pulsed flight between the reference circular orbit of an artificial Earth satellite and the target elliptical orbit with a phase restriction on the maximum distance of the spacecraft from the Earth has been solved. Derivatives under the transversality of Lagrange principle in the process of solving are calculated by means of a specially developed technology of numerical-analytical differentiation. The first part of the paper introduces the statement and formalization of the problem. The second part of the paper studies the conditions for the optimality of Lagrange principle, analyses them and compares the findings obtained with the previously known results.