An explicitly restarted symmetric Lanczos algorithm described in this paper belongs to a class which is (theoretically) equivalent to its implicitly restarted alternative. Its main merit is that it is simpler to use. The proposed variant minimizes the cost of the restart by retaining many ``older'' Ritz vectors, and optimizes their selection. A number of numerical experiments is presented. The loss of the orthogonality (which is well know to require a reorthogonalization) is dealt with by using an economical partial reorthogonalization scheme.