We revisit (un)soundness of transformations of conditional into

unconditional rewrite systems. The focus here is on so-called

unravelings, the most simple and natural kind of such

transformations, for the class of normal conditional systems without

extra variables. By a systematic and thorough study of existing

counterexamples and of the potential sources of unsoundness we

obtain several new positive and negative results. In particular, we

prove the following new results: Confluence, non-erasingness and

weak left-linearity (of a given conditional system) each guarantee

soundness of the unraveled version w.r.t. the original one. The

latter result substantially extends the only known sufficient

criterion for soundness, namely left-linearity. Furthermore, by

means of counterexamples we refute various other tempting

conjectures about sufficient conditions for soundness.