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It was shown in (Verlan, 2005) that complexity measures for insertion-deletion systems need a revision and new complexity measures taking into account the sizes of both left and right context were proposed. In this article we investigate insertion-deletion systems having a context only on one side of insertion or deletion rules. We show that a minimal deletion (of one symbol) in one-symbol one-sided context is sufficient for the computational completeness if a cooperation of 4 symbols is used for insertion rules and not sufficient if an insertion of one symbol in onesymbol left and right context is used. We also prove the computational completeness for the case of the minimal context-free deletion (of two symbols) and insertion of two symbols in one-symbol one-sided context.