We present a feasibility study for the task of finding and expanding enthymemes, i.e, arguments with missing propositions, in real-world texts. We split the task into three subtasks: 1. finding the beginning and the end of the text span describing a minimal argument block, 2. deciding whether that span really represents an enthymematic minimal argument block, and 3. describing the missing premise in natural language. We argue that an objective ground truth for these tasks must be found before we can address automatic annotation. In our opinion, such a ground truth can only come from agreement on independent human annotation. In other words, we require that two or more annotators agree on the existence and textual span of an enthymematic minimal argument block, and on the actual paraphrase of the missing premise. We present a case study using the two authors of this paper as annotators, where we test three cue phrases for their suitability to this task, because, therefore and let alone. We find that minimal argument blocks centred around the cue phrase let alone are of a particularly high quality. We also discuss pragmatic effects of let alone and how they relate to argumentation theory.