We consider graph-controlled insertion-deletion systems and prove that the systems with sizes (i) (3; 1, 1, 1; 1, 0, 1), (ii) $$(3;1,1,1;1,1,0)$$ and (iii) (2; 2, 0, 0; 1, 1, 1) are computationally complete. Moreover, graph-controlled insertion-deletion systems simulate linear languages with sizes (2; 2, 0, 1, 1, 0, 0), (2; 2, 1, 0; 1, 0, 0), (3; 1, 0, 1; 1, 0, 0), or (3; 1, 1, 0; 1, 0, 0). Simulations of metalinear languages are also studied. The parameters in the size $$(k;n,i',i'';m,j',j'')$$ of a graph-controlled insertion-deletion system denote (from left to right) the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; a similar list of three parameters concerning deletion follows.