Both of those were the work of Don Bluth, an ex-Disney guy that left because their quality/management was so crap in the 80's. He is also responsible the Secret of Nymph among others.
But there was a lot of good traditional animation outside of Disney and Bluth. Fox cranked out a few, like Anastacia and Titan AE.
Both of those were Don Bluth.
Some Don Bluth films I forgot to mention:
- Rock-a-Doodle (bad)
- All Dogs Go To Heaven (strange)
- A Troll in Central Park (haven't seen)
- The Pebble and the Penguin (haven't seen)
Then there were a few independant cartoon movies, like the excellent The Brave Little Toaster.
That was definitely Disney (OP was asking for non-Disney examples). Yes, the John Lassetter connection was evident in that movie.
Not sure who made this one:
- Cat's Don't Dance (though this was pretty good when I saw it in the '90s)
I'm not sure whether to classify "Who Framed Roger Rabbit" as an animated movie or a Disney movie. It's a strange combination in every respect. Steven Spielberg's involvement makes it feel like a Universal production, but Disney definitely had a lot to do with the distribution and marketing. Roger Rabbit became Disney's character.