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The optimal transmission switching (OTS) problem, a mixed-integer program (MIP), has been proposed as a way to choose lines to take out of service to reduce generation costs. One impediment to the use of OTS in practice is the very long computing time to solve it. This paper proposes two heuristics which rely on a line-ranking parameter that is based on the optimal solution to the ordinary dc optimal power flow problem, a linear program (LP). One heuristic solves a sequence of LPs, removing one line at a time, and the other heuristic solves a sequence of MIPs, removing one line at a time, and each MIP has far fewer binary variables (for switching the lines out of service) than the original MIP. The proposed heuristics are tested on 118-bus and 662-bus systems, and compared with the most common previous heuristic in the literature, which solves a sequence of MIPs, removing one line at a time, with each MIP having all binary variables, i.e., one for each line. Both heuristics are much faster than the previous heuristic from the literature. In almost all cases tested, both proposed heuristics find cost reductions that are approximately as large as the previous heuristic. The computing time reductions are so great that OTS may now be practical with respect to the computing time issue.