Mariah Carey had plenty to prove in 2005, before the release of what many call her comeback album, “The Emancipation of Mimi.” In 2001, she released the semi-autobiographical film and soundtrack “Glitter,” which flopped critically and commercially, and appeared on MTV’s “Total Request Live” wearing only a T-shirt, shrieking and jumping in front of a bemused Carson Daly. The following year, Ms. Carey released “Charmbracelet,” which made only a modest impact chart-wise. She bounced from label to label, leaving Sony/ Columbia for Virgin Records and a record $80 million contract, only to be bought out by that label before finally signing with Island Records.

Today, the 38-year-old Ms. Carey is standing on her own two feet again, having weathered the comeback trail, with the release of her 10th full-length album, “E=MC2 .”

In the 1990s, Ms. Carey and her incredible vocal range were as stable a force as the pop world knew, charting at least one no. 1 single in each year of that decade. As the ’90s progressed, she shifted gradually from a Motown-inspired, adult-contemporary style to a pop-oriented sound defined by upbeat singles such as “Dreamlover” and power ballads such as “Hero” and “One Sweet Day.” In 1997, with the release of “Butterfly,” she underwent further reinvention by turning toward hip-hop.

The rapper Lupe Fiasco wrote the line “Hip-hop saved my life,” and certainly for Ms. Carey, the genre was generous to her during her “Mimi” period: Where the debacles of “Glitter” and “Charmbracelet” had forced listeners to suffer through cheesy, unwieldy pop songs and undermined Ms. Carey’s ability to take a simple melody and lift it with the power of her voice, the producer Jermaine Dupri revived her balanced vocal touch on “Mimi,” toning down the top-note touches with the singles “We Belong Together” and “Shake It Off.” The former, especially, highlighted Ms. Carey’s ability to create a mournful tone with her voice, and signaled an important transition as she took on the role of narrator of pain rather than participant in it.

The attention paid to the “Mimi” follow-up has been eager, and the biggest public question related to “E=MC2 ” has been: Can any of the songs come close to the power of “We Belong Together”?

Not quite, but neither is that the right question to ask about this album. Ms. Carey (who knows a thing or two about hit singles: With the lead single off “E=MC2 ,” “Touch My Body,” she passed Elvis Presley for the second-most no. 1 singles of all time) should be applauded for not recording just another batch of songs in the mold of “We Belong Together.” “Mimi” was certainly more of a collection of singles that were bound for the radio or the club, rather than a thematic album. That’s not to say that “E=MC2 ” is much more cohesive; there are some throwaway pop tracks, which is to be expected of any hiphop-oriented album (“I’m That Chick” and “Side Effects” come to mind). But there is a kind of wholeness to the album, a sense that Ms. Carey has come full circle in her genre-hopping and vocally acrobatic habits.

The best parts of “E=MC2 ” are the surprises, though “Touch My Body” is not one of them: It’s a smooth, mid-tempo song with a swaying, melodic beat, and serves as a simple and mellow introduction to the material. A much stronger song is the album’s opener, “Migrate,” a hip-hop track about conscious independence on which Ms. Carey sings about living her life without any attachments. Sung in sassy tones over a repeating, upbeat chorus, it’s the kind of assured single one would expect from R. Kelly, who’s known in no small part for his macho tendencies. “Migrate” displays a confident, social forwardness that is new to Ms. Carey, but it’s one that she manages proudly. She’s no longer looking for a “Dreamlover” to come and rescue her, as she did in 1993: In “Migrate,” she’s already rescued, and enjoying the after-party.

Ms. Carey dabbles in reggae on “Cruise Control,” a song produced by Mr. Dupri and featuring vocals by Damian Marley. Any chorus that features a spelled-out word (in this case, “c-r-u-i-s-e”) could enter the territory of being too cute, but Ms. Carey grooves deeply with the line, giving the song an urbane feel. On “I’ll Be Lovin’ U Long Time,” her voice is supplemented by a brassy disco sample (DeBarge’s “Stay With Me”), and she again sings in a deep and soulful tone, channeling the sophistication of Erykah Badu in a sweet, lyrical song about devotion.

For longtime fans of Ms. Carey, though, the very last song on the album is a throwback to a time before debacles and debauchery marred the singer’s public image. The song builds its strength on Ms. Carey’s Motown inclinations, as she mixes lyrics about independence with references to biblical passages. “I Wish You Well” closes the album on a note of maturity and balance. By revisiting the vocal tones and subject matter of her early career, Ms. Carey leapfrogs the tentative steps she took in “Mimi” to win back fans, and instead creates an album that looks her fans in the eye and tells them that she intends to never fall back down.