Three out of the four members in Kings of Leon are brothers who grew up on the road with their traveling evangelical father (the other Leon is a cousin). But this is no Sunday school music, with lyrics like “C-nts watch their bodies, no room for make up” (“Taper Jean Girl”). Not to say vulgarity is the issue on the Nashville-bred band’s sophomore effort, but unintelligible and mindless lyrics might be. Another glaring problem is a big handful of lackluster, uninspired tunes (“Girl” is one of them) — though the album is saved from the abyss of mediocrity by bursts of melodic ingenuity.

Two years after their hyped-up debut, “Young and Young Manhood,” the young men of Leon still have bad hair and bad album names. At least this time around, they have more dynamic music. The age-old comparisons to The Strokes that abounded after “Manhood” don’t apply here, as the band emerges with a sound that’s distinctly its own. Twangy, erratic guitar riffs led by Jared Followill’s forceful bass power the upbeat tracks of “Heartbreak,” whereas their debut (as well as the wonderful “Holy Roller Novocaine” EP) was indebted to your standard alt-country-meets-alt-rock aesthetic.

Although the band has matured since 2003, their sound still has loose ends under lead-singer Caleb Followill’s incredibly affected vocals. His voice lacks the genuine charm, or endearing sweetness, of other historically bad singers like Dylan, Tom Waits or AC/DC’s Bon Scott. Caleb sings emotionally, but he sounds like he’s trying too hard to sound special — mumbling his words in a lazy, gravelly drawl that renders his lyrics incomprehensible. Before breaking into painful yodeling on “Day Old Blues,” Caleb sings: “Girls are gonna love the way I toss my hair/ Boys are gonna hate the way I seem.” He’s right about one thing.

That the lyrics are garbled actually helps the album, because the listener can’t hear how horribly ridiculous they are. But after a few listens it becomes clear that the band trades literate depth for sleazy playfulness.

On “Soft,” Caleb explains, “I’d pop myself in your body/ I’d come into your party, but I’m soft.” Neither deep nor pleasant. Even on one of the album’s best tracks, the manic “Milk,” Caleb croons: “She saw my comb over, her hourglass body/ She had problems with drinking milk/ And being school tardy.” At least the lines make the album title seem eloquent.

But while its lyrics could use work, “Milk” stands as an excellent track. Caleb’s moaning over a thumping guitar perfectly demonstrates that the band can really get it right melodically. Beginning softly with quiet acoustic resonance, the song ebbs and flows into a bass-fueled, addictive chorus.

The instrumentation is the salvation of the disc. The garage-rock “Bucket” (where they actually use the phrase “Kick the bucket”), boasts an impeccably slow breakdown between each verse. “King of the Rodeo,” the catchiest song on the album (complete with rhythmic clapping), has Caleb rapidly spitting out the melodic chorus over a Franz Ferdinand-inspired electric guitar. The bass and guitar combination is stellar on “Razz,” droning at first but eventually elevating to a swinging rhythm. By the way Leon handles its instruments, it’s obvious they have the rock and roll down.

The enigma, then, is the lack of excitement on a disc with so many upbeat, urgent songs. Perhaps it is because the band is ultimately uninspired, lyrically immature and stylistically insincere. Yet “Heartbreak” nevertheless gets better with each listen, as an enjoyable, albeit distorted, experience. The album’s sound both shines and wavers, but at least the Brothers Leon can say the sound is completely theirs.