A straightforward heuristic-oriented method for stream tearing is proposed in this work. It does not use the traditional methods of evolutionary process-cycle analysis. First, an edge (stream) weighted spanning-tree is constructed from the process graph using weights based on the 'in' and 'out' degrees of the process digraph vertices. Second, a directed acyclic graph (DAG) is constructed such that it is the maximum edge (stream) acyclic sub-set of the process digraph. The DAG is constructed by adding ('put-back'), where possible, directed edges (streams) not already in the spanning-tree. A hierachial ordering based on the same preferential weighting system as the spanning-tree determines the sequence of the 'put-back' trials. The remaining edges which cannot be 'put-back' into the DAG form a tear set. The weighting system used formed a minimal cardinality tear set in all of the examples tested. Pre-partitioning of the network into strongly connected components is not required and a node computational order is easily derived. Further, the method is extended to produce tear sets which minimise another set of stream weights, in this case the variables per stream. While the scheme proposed in this paper is heuristic-oriented, most of its methods are contained in classical graph theory and are consequently easily reproduced with efficient algorithms.