When Mystic Braves recorded their first two albums, they took the “bang the tracks out live and then sing overdubs and call it a wrap” approach, singer Julian Ducatenzeiler says. The Los Angeles group was more deliberate in making the follow-up, “Days of Yesteryear,” which premieres today on Speakeasy.

The 10-track psych-rock album sounds like a forgotten gem from the late ’60s that turned up at the back of some paisley-filled closet in the Electric Prunes’ basement. The songs are full of Farfisa organ, quavering guitars and...