functional style - FoldWhile and FoldWhileList

Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in FoldWhile or a FoldWhileList. So, since these constructs seem useful to me, I have tried to brew my own. Here are my current implementations. Anyone have suggestions on how either of these might be improved. I'd be particularly interested in a variant of FoldWhile that did not require as much memory as FoldWhileList.

 FoldWhileList[f_, init_, list_, test_, m_, max_] := 
 Block[{i = 0}, 
    NestWhileList[(i = i + 1; f[#, Part[list, i]]) &, init, test, m, max]]

and

 FoldWhile[f_, init_, list_, test_, m_, max_] := 
    Last[FoldWhileList[f, init, list, test, m, max]]