Jennifer Hudson is still searching for songs to do right by her voice. (Larry Busacca/Getty Images)

In the long-ago ingenue days of Whitney and Mariah, songs were of secondary importance, merely propulsion devices for heavenly voices. But in an iTunes world, songs are everything, and Hudson, whose sophomore disc, “I Remember Me,” drops Tuesday, hasn’t yet made the hit song she’ll be remembered for. Or any hit song at all.

It may be that Hudson just wasn’t made for these times. She has a voice built for retro — for gospel songs and torch songs, for Broadway numbers such as her rafter-shaking cover of “And I Am Telling You I’m Not Going.” It’s a voice built for just about anything, it turns out, but the contemporary hip-hop-informed R&B songs that will get her played on the radio. On her 2008 self-titled debut, she was miscast as a too-urban diva, at the mercy of a kitchen-sink assortment of trends that included a three-way duet with T-Pain and a vocoder; in an ideal universe, Hudson would never need to know T-Pain even existed.

“I Remember Me” doesn’t entirely rectify the problem: Anyone waiting for a great song to happen to Jennifer Hudson will still be waiting when it’s over. It’s not for lack of trying, since Hudson’s collaborators are the usual roving team of pop-cultural first responders, such as songwriter Ryan Tedder and producers Rich Harrison and Stargate. They’ve armed Hudson with pop songs that feel natural (such as the truly fine Alicia Keys/Swizz Beatz collaboration “Angel”), dance songs informed more by Studio 54 nostalgia than by Lady Gaga (the disco burner “Everybody Needs Love”) and slow songs that aren’t overwrought (“Where You At,” penned by R. Kelly, unlikely king of the schmaltzy yet unembarrassing R&B power ballad).

“I Remember Me” is Hudson’s first release since the 2008 murder of three of her family members, a topic addressed only vaguely on tracks such as the unremarkable “Still Here,” a standard Diane Warren Triumph Over Adversity ballad recycled from Natasha Bedingfield. It’s otherwise a stunningly upbeat collection, capable of the occasional surprise: a cover of Brooks & Dunn’s “Believe” reworked as a gospel roof-raiser; a stalker anthem (“Don’t dare /Send me straight to voice mail / Babe I’m just gonna text you / Hope it ain’t no issue”) tucked neatly inside a stutter-beat love song (“No One Gonna Love You”).

Hudson dispatches even the most technically difficult tracks as if she were swatting away flies, her unblinking confidence reminiscent of Adele, another big-voiced, retro-inclined singer on a perpetual hunt for songs worthy of her. To witness Hudson whoop, holler, trill and testify her way through even this pretty-good assortment of R&B songs is a thrill. She may not have found her signature song, but she’s getting closer.

Recommended tracks: “Everybody Needs Love,” “Angel,” “No One Gonna Love You”