One of my favorites: Sweetheart of the Rodeo. The Bryds were decidedly psychedelic, and for whatever reason let Gram Parsons make an album for them. Well worth the listen even if you're not into country music.
They barely let Gram Parsons make an album for them -- they fought with him during its creation, and he left before it was released. Because he immediately formed The Flying Burrito Brothers with Chris Hillman, another Byrd, I suspect Hillman was an ally in trying country after five psychedelic albums. Remember, this was an era when musicians were fleshing out what rock music could be (you can see this in the Beatles' 1960s albums from simple poppy songs to Indian drones, jazz chords, and multitrack madness) and seeing what else you could cut it with (Indian, folk, etc.).
In that spirit, the self-titled album, The Great Speckled Bird, is worth checking out. The songwriters and vocalists are Ian and Sylvia, probably most famous for Four Strong Winds.