Two periods of phenomenal success have obscured Rivers Cuomo’s true status as a pop eccentric, a singer/songwriter whose ear for oddity is as sharp as his ear for melody. Success has the tendency to make the unusual seem common, but that wasn’t quite the case with Cuomo, as Weezer’s hits rarely showcased his wayward traits: they were so hooky, so anthemic that they roped in millions of listeners that never might have dug deeper into the albums, discovering his heartbroken ballads and skewed humor. The latter was certainly evident on the band’s big 1994 breakthrough “Buddy Holly,” which helped kick off Weezer’s first period of great success, but the cuteness of the chorus led some detractors to peg the group as novelties, thereby ignoring the great songwriting that fueled “Buddy Holly” and the rest of their debut album. That novelty reputation dogged them throughout their extended late ’90s hiatus but when they returned in 2001 with another eponymous album, they kicked off a second great period of popularity, one where they banished the novelty tag but once the band became a working concern again, releasing albums regularly, many fans carped that the band — meaning Rivers — had become too predictable, favoring big rock hooks to the idiosyncratic pop of Pinkerton, the 1996 sophomore album that bombed commercially yet remains most beloved of all hardcore Weezer fans, as it retained much of the quirkiness of the debut yet punctuated it with Cuomo’s most emotionally naked songwriting.

Neither camp — either the detractors or the too-fanatical fans — spent much time considering how the writer behind Pinkerton was also the one behind the glossy, pumped-up Make Believe, how each was completely Cuomo at its core. Pinkerton is the romantic version of Rivers, the geek pouring his heart out on page, while Make Believe is the determined, professional songwriter, the one who carries around a notebook with dissections of popular songs, figuring out what works and what doesn’t. Both are equally true and both are on display on the quite terrific Alone: The Home Recordings, a 2007 collection of 18 demos recorded between 1992 and 2007. Although this is heavily concentrated on ’90s recordings — including a big chunk of songs from the scrapped sequel to the Blue Album, Songs from the Black Hole — that professional songwriter creeps out, as it’s possible to hear Rivers working out the mechanics of what makes a song work by covering three writers most musicians wouldn’t connect: Gregg Alexander before he was a New Radical (”The World We Love So Much”), Ice Cube (”The Bomb”), and Dion (”Little Diane”). There isn’t irony here, not even on the clattering noise of “The Bomb” — there’s excitement in the sound and curiosity about how it’s constructed, and as the collection starts to reach the present toward its end, it’s possible to hear Cuomo trying to write songs that fit within these classicist forms, especially on the open-hearted power ballad “I Was Made for Loving You” and “This Is the Way,” whose icy drum-machine beats give it a vague adult-pop feel.

These latter-day trends are what rankle some Weezer true believers, but they’re not only sturdy songs, they make sense when presented as part of Cuomo’s progress in Alone, and they also fit nicely amidst the ragged unreleased cuts from the ’90s. These tunes are clearly demos — the audio quality fades in and out, sometimes things sound stripped down and perhaps the arrangements are not fleshed out, but these songs are fully formed and, if they had been given full Weezer treatment, they would have fit on either the Blue Album or Pinkerton. But it’s better to hear them in these rough incarnations as Cuomo’s gifts shine through brighter this way: his humor flows naturally, his heartbreak is sweetly melancholy, and his melodies hook into the subconscious. It’s not just that the songs are all strong, but these rough arrangements are emotionally resonant and sonically varied. The latter is especially welcome, as Weezer’s new millennium comeback, for all of its highlights — and there are many, even on the maligned Rick Rubin-produced Make Believe — has been monochromatically rock, where Alone is filled with shade and texture. Perhaps Weezer will have a touch of this color on their next studio album, but if they don’t, that’s fine: Cuomo’s increasing songcraft will pull him through, and Alone will stand as an idiosyncratic gem in his catalog, showcasing him at his eccentric best.