Diet Cig’s delightful singer-guitarist Alex Luciano knows her power.

Throughout the New Paltz duo’s debut, “Swear I’m Good at This” (Frenchkiss), Luciano tells poignant, confessional tales in a sweet, conversational tone. But when she needs to hammer a point home — and there are plenty of them here — Luciano switches to a commanding, full-throated voice or a hard-rocking guitar riff. When we’re lucky, it’s both.

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In “Link in Bio,” Luciano is equal parts Juliana Hatfield and “Exile in Guyville”-era Liz Phair, as she rails against the double standard women suffer on social media. “I’m done with being a chill girl,” she declares during a lull in her bouncy guitar frenzy. “I’m trying to take over the world.”

The first single, “Tummy Ache,” is a potent indie-pop anthem, but it comes with a price. (“My stomach hurts, ’cause it’s hard to be a punk while wearing a skirt” is Luciano’s refrain.)

The album’s best moment comes in the opener, “Sixteen,” after Luciano reveals an embarrassing dating moment. She pauses and asks, “Ready?” before launching into a furious declaration of independence accompanied by roaring guitar and Noah Bowman’s bashing drums. Oh yes, Alex, we have been waiting for this.