They just keep coming to my head...
OK, if you like EH, then The Abyss? When a crew member drowned he gave one of the most emotional yet believable performances I have ever seen. Right up there with Robert Di Niro in The Mission - A former slave trader of South American indigenous peoples joins the Jesuits (?) on a mission of conversion in an effort to gain Heavenly absolution for a grievous sin. When he meets up with a tribe that he formerly took slaves from, he loses a great amount of weight that he has been carrying - both literally and figuratively, and Di Niro's scene of redemption is one I haven't forgotten.
I've watched Abyss.
The other movie should be The Mission (1986). I have had it in my list for more than 2 years and haven't had the chance yet. I just searched my local rental shop. It seems that they have it on DVD. I'll watch it this Sunday. If it's not the movie you're describing I have to search more.
Thanks again.