The authors investigate some problems of efficient analytic continuation of power series in the plane \(\mathbb C\) by means of summability methods. They describe a new class of sets differing from domains allowing efficient summation (Theorem 1). In Section 3 they prove the existence of such matrix summation methods that are sufficient for the restoration of the analytic continuation of power series in a fixed point of a domain \(\Omega \subset \mathbb C\) without any additional conditions on \(\Omega.\)