The importance of efficient software testing procedures is driven by an ever increasing system complexity as well as global competition. In the particular case of manual test cases at the system integration level, where thousands of test cases may be executed before release, time must be well spent in order to test the system as completely and as efficiently as possible. Automating a subset of the manual test cases, i.e, translating the manual instructions to automatically executable code, is one way of decreasing the test effort. It is further common that test cases exhibit similarities, which can be exploited through reuse when automating a test suite. In this paper, we investigate the potential for reducing test effort by ordering the test cases before such automation, given that we can reuse already automated parts of test cases. In our analysis, we investigate several approaches for prioritization in a case study at a large Swedish vehicular manufacturer. The study analyzes the effects with respect to test effort, on four projects with a total of 3919 integration test cases constituting 35,180 test steps, written in natural language. The results show that for the four projects considered, the difference in expected manual effort between the best and the worst order found is on average 12 percentage points. The results also show that our proposed prioritization method is nearly as good as more resource demanding meta-heuristic approaches at a fraction of the computational time. Based on our results, we conclude that the order of automation is important when the set of test cases contain similar steps (instructions) that cannot be removed, but are possible to reuse. More precisely, the order is important with respect to how quickly the manual test execution effort decreases for a set of test cases that are being automated.