Recent efforts toward theorising the role of serendipity (that is, accidental or chance-based findings) in scientific discovery encounter an inevitable problem with the data available: most of it is in narrative form, and anecdotal, and thus presents not only case-by-case variability but great potential for rhetorical bias. At least, a positive bias exists, given that instances of missed or failed serendipity are (one assumes) drastically under-represented in the literature, having not led to discovery despite their potential. Accumulating more instances (anecdotes), and nearer to the point of occurrence, in favour of continuing to use apocrypha like the story of Archimedes in the bath, is one way to improve on the theory we can derive from the experience and practice of scientists; to this end, a new series in the Journal of Trial and Error began last year. For this talk, I look to how (or whether) the theory presented by myself and colleagues in this series so far, derived from analysis of empirical cases, takes into account issues of rhetorical justice relevant to the utilization of anecdotes to theorize the structure of scientific discovery.