In on-line computation, instance of the problem dealt is not entirely known from the beginning of the solution process, but it is revealed step-by-step. In this paper we deal with on-line independent set. On-line models studied until now for this problem suppose that the input graph is initially empty and revealed either vertex-by-vertex, or cluster-by-cluster. Here we present a new on-line model quite different to the ones already studied. It assumes that a superset of the final graph is initially present (in our case the complete graph on the order n of the final graph) and edges are progressively removed until the achievement of the final graph. Next, we revisit model introduced in [M. Demange, X. Paradon and V. Th. Paschos, On-line maximum-order induced hereditary subgraph problems, Proc. SOFSEM 2000—Theory and Practice of Informatics, LNCS 1963, pp. 326–334, 2000] and study relaxations assuming that some paying backtracking is allowed.