The thesis of underdetermination presents a major obstacle to the epistemological claims of scientific realism. That thesis is regularly assumed in the philosophy of science, but is puzzlingly at odds with the actual history of science, in which empirically adequate theories are thin on the ground. We propose to advance a case for scientific realism which concentrates on the process of scientific reasoning rather than its theoretical products. Developing an account of causal–explanatory inference will make it easier to resist the thesis of underdetermination. For, if we are not restricted to inference to the best explanation only at the level of major theories, we will be able to acknowledge that there is a structure in data sets which imposes serious constraints on possible theoretical alternatives. We describe how Differential Inference, a form of inference based on contrastive explanation, can be used in order to generate causal hypotheses. We then go on to consider how experimental manipulation of differences can be used to achieve Difference Closure, thereby confirming claims of causal efficacy and also eliminating possible confounds. The model of Differential Inference outlined here shows at least one way in which it is possible to ‘reason from the phenomena’.