Well, surely we're all expressing personal preferences here, and the thread specifically relates to Jeannie so I'm quite comfortable giving my choices (without disparaging any other singers!).

In no particular order -- Harlaw, Son David, Lord Randal/Darnal, Matty Groves, Three Gypsies.

What I remember was the difference between the more driven or direct narratives (with their variety of pace and tone) and the inevitable, unwelcome doom of the repetitious, tragic ballads with their sonorous tone and ever-slowing pace.

Jeannie was a true story-teller -- she would transfix you in an audience whilst delivering a verse or two of the story before choosing the next recipient!