Abstract. Current network flows heuristics for cell suppression in positive tables (i.e, cell values are greater or equal than zero) rely on the solution of several minimum-cost subproblems. A very efficient heuristic based on shortest-paths was also developed in the past, but it was only appropriate for general tables (i.e., cell values can be either positive or negative), whereas in practice most real tables are positive. The method presented in this work overcomes the lacks of previous approaches: it is designed for positive tables and only requires the solution of shortestpaths subproblems. It follows that it is orders of magnitude faster than previous network flows heuristics. We report an extensive computational experience in the solution of two-dimensional tables, either with or without hierarchical rows, of up to 250000 and 500000 cells, respectively.