Among the most promising Minneapolis indie bands to emerge in the past five years, Bad Bad Hats are in the process of reigniting their initial buzz. In 2013, their breakout EP, It Hurts, introduced new fans to singer-guitarist Kerry Alexander’s curlicue melodies, lyrics about being in (or out) of love, and jaunty indie-pop instrumentation, rounded out by bassist Noah Boswell and drummer Chris Hoge. Their more varied and confident 2015 debut album, Psychic Reader, featuring the stomping anthem “Fight Song,” helped the band top City Pages’ Picked to Click poll that year and was ranked as the second best Minnesota album in the Star Tribune’s Twin Cities Critics Tally. They haven’t released so much as a single since then, but this August they announced they’d finished mixing the follow-up. On Saturday, Bad Bad Hats will play a doubleheader at the Entry: an all-ages show starting at 5 p.m. (featuring opening act Idle Empress) to be followed by an 18+ gig at 9 (with support from Jessica Manning).