Here's my list of the five best non-Disney animated film scores, non-musical edition. List is in chronological order, not ranked. Note that excluding musicals eliminated one entry: Jimmy Webb, The Last Unicorn (1982).

1) James Horner, The Land Before Time (1988): Horner wrote the best score of his prolific career for this Don Bluth animated classic. This is one of my top three scores of all time.