Maybe 'elegance' isn't the right word. Maybe it's 'economy'. Or 'scope'. Either way, I find that I am more impressed by an alternate history that doesn't use a big battle as its point of change (double points if it doesn't use anything that happened during the Civil War or World War II -- I am sick to death of both types of AH stories), in favour of a smaller or more discrete difference.
Example of economy: although not technically an alternate history (more of an alternate society), Wen Spencer's A Brother's Price envisions a different set of gender roles resulting from an increase in male infant mortality (or possibly fewer successful impregnations that result in males...Spencer is a bit vague here). It's an 'economical' change because it's a tweak to something that's already known -- that male infants have a lower survivability than female (we get more males than females only when prenatal care is good) -- which completely changes the society in believable ways (to oversimplify Spencer....if there's only one man for every 10 to 12 women, there's no way in heck that the women are going to let that man out of the house, and certainly are not going to let him fight, or carry a weapon).
What else can we change in an 'economical' fashion? More (but still sporadic) European contact with North America? Earlier discovery of penicillin (or, conversely, much later)? The 1949 Newfoundland referendum goes the other way?
Example of economy: although not technically an alternate history (more of an alternate society), Wen Spencer's A Brother's Price envisions a different set of gender roles resulting from an increase in male infant mortality (or possibly fewer successful impregnations that result in males...Spencer is a bit vague here). It's an 'economical' change because it's a tweak to something that's already known -- that male infants have a lower survivability than female (we get more males than females only when prenatal care is good) -- which completely changes the society in believable ways (to oversimplify Spencer....if there's only one man for every 10 to 12 women, there's no way in heck that the women are going to let that man out of the house, and certainly are not going to let him fight, or carry a weapon).
What else can we change in an 'economical' fashion? More (but still sporadic) European contact with North America? Earlier discovery of penicillin (or, conversely, much later)? The 1949 Newfoundland referendum goes the other way?
Hmm. I'm thinking about alternate science, I realize, when I'm thinking of penicillin. Howzabout proper sewage? The Romans knew, then everyone forgot, but the technology is simple (albeit labor-intensive) to implement years or even centuries before (or after) Joseph Bazalgette was commissioned to save London's ass. 
