The Pierces are Alabama-born sisters Catherine and Allison, who moved to New York City when their dream of becoming ballerinas didn’t pan out. At first, music didn’t look like it would yield much, either: Despite the siblings’ good looks and helpful connections (Catherine has been romantically involved with Albert Hammond Jr.), the first two Pierces albums — both humdrum folk-pop affairs that made Michelle Branch sound daring — went nowhere.

Yet Thirteen Tales of Love and Revenge unveils a new and vastly improved sister act, one that should earn the Pierces a place alongside fellow Big Apple eccentrics like Nellie McKay and Regina Spektor. Strummed acoustic guitars and pretty vocal harmonies still dominate, but here they’re liberally decorated with the detritus of the Lower East Side surroundings: gypsy-punk strings, dance-rock grooves, hip-hop beats. Seemingly terrible ideas somehow succeed: “Lies” remakes Gwen Stefani’s “Rich Girl” as an antifolk shuffle; “Boring” is bar-band electroclash; “Lights On” layers new-wave keyboards over country twang.

This stylistic schizophrenia perfectly suits the Pierces’ songs, which alternate caustic hipster banter with unguarded vulnerability. For example, in “Kill! Kill! Kill!” you expect B-movie bravado, but get raw desperation instead: “It’s killing me that I’m still in love with you,” Catherine admits. It’s just one more surprise on a record full of them.