No false advertising anywhere on the cover of the newest entry in Bob Dylan’s “Bootleg Series” about which era is being covered. The boxed set’s subtitle lays out the dates — 1980-85 — but even before you land on the fine print, there’s the period-specificity of the cover photo, a vintage Ken Regan shot of a suave Dylan with his shirt seductively unbuttoned to give us just a little then-de-rigueur chest-hair action. Ironically, maybe, there are some Dylan fans who think of this as the era when he was at his least seductive, purely musically speaking. To this way of thinking, if there were a Rolling Stone cover line to accompany that photo, it might be: “He’s hot, he’s sexy and he’s foundering in his mid-period.”

And then there are those of us who find Dylan’s 1980s about as interesting as any other post-‘60s decade of his, once you dig past the admittedly spotty studio albums and explore the often superior alternate takes of material that didn’t completely work on record, or the great songs that never came out at all at the time. Some of this archival material from the ‘80s was already the basis of Dylan’s very first official “Bootleg” release 30 years ago; think “Blind Willie McTell,” the infamous “Infidels” discard that did more than any other one song to ensure fans that the series would be an invaluable source of new/old Dylan material for years and decades to come. Unofficial bootlegs have also served as a seemingly bottomless tease for what might deserve to come out of the vault. Now we get a fuller look at that time in the five-CD “Springtime in New York: The Bootleg Series Vol. 16 (1980-1985),” which might be in the odd position of being the least anticipated of these annual exhumations for some fans but one of the most eagerly awaited for others.

One thing that makes “Springtime in New York” harder to summarize than most of Dylan’s other retrospective boxed sets is that it covers a wealth of unheard material from the sessions for three albums that, while sequential, don’t really have huge commonalities between then. First up in the docket is 1981’s “Shot of Love,” which felt raw and undercooked at the time it was released. The last covered in this three-album overview is 1985’s “Empire Burlesque,” which, in contrast, was overbaked… or over-Arthur-Baker-ed, to invoke the name of the producer who took a lot of the heat for that record’s inadequacies. Sandwiched in between them was 1983’s “Infidels,” probably the most generally well-regarded album Dylan made between “Blood on the Tracks” in the mid-‘70s and “Oh Mercy” at the end of the ‘80s. As one of about a hundred supposed comebacks he’s had over the years, “Infidels” benefitted in popular perception by being a more definitive break from the “born again” years, after “Shot of Love” seemed to have one foot in and one foot out… and also benefitted from being, like, actually quite good, of course.

But even “Infidels” had its flaws, one of which was its brevity — only eight songs made the cut, which seemed triply egregious once the “Bootleg Series” got underway in the early ‘90s and fans found out that Dylan’s foggy self-curatorial judgment had led him to leave some of the best stuff he was writing on the cutting room floor. The second problem, more glaring in hindsight, was a lousy drum sound that by 1983 had become so obligatory in rock that even Bob Dylan records had no vaccine against it. There are moments on “Infidels” that are chugging along quite tastefully under the tutelage of co-producer Mark Knopfler when cometh an electronically filtered tom-tom fill so of its misguided era that it’s as if Freddy Krueger suddenly dragged his nails across a chalkboard for a few seconds. The problem only became compounded on “Empire Burlesque,” which went further in submitting perfectly good songs to the full Freddy effect — like the unlistenable original-release version of “When the Night Comes Falling From the Sky” — complete with swing-less snare hits that sound like muffled cannon blasts. It only took a little over 35 years to get alternate mixes or takes of most of the songs from these two albums that undo the datedness and return these tracks to the realm of timelessness. It’s like hearing the real “Seeing the Real You at Last” … at last.

Valuable as it is to be getting near-soundalike versions of so many of these tracks that strip away the ‘80s gloss, that’s only the smaller part of why “Springtime in New York” is a treasure trove. For folks who don’t obsess over the horror of gated-drum sounds, and maybe the rest of us, too, there are the covers, the originals that never made it onto any Dylan album, and the early versions of familiar tunes that sport radically different lyrics, arrangements or even melodies. It’s worth noting that while the single disc devoted to “Empire Burlesque” consists almost entirely of alternate versions of that album’s tracks, the first two discs in this set, which are both devoted to the “Shot of Love” era, only touch down on a single song from that album (“Lenny Bruce Is Dead”), since there’s so much else to draw upon. (The two discs devoted to “Infidels” fall somewhere in between, offering a little bit of everything.)

If there were a fire and I could rescue just two discs from this five-CD set, it’d be those first couple devoted to “SoL” circa 1980-81. I’m hearing from some other folks that those are their two least favorite in the set, and they’d just as soon get on with the “Infidels” era post haste. Needless to say, everyone’s Dylan mileage may vary. Disc 1 in particular is a rootsy marvel, consisting almost entirely of rehearsals — captured in prime studio-quality sound — for the first tour Dylan did after the outings that consisted strictly of his Christian material. He’s playing with probably the best live band he ever had (including Fred Tackett, Tim Drummond and Jim Keltner), along with the best crew of female backup singers he ever employed, and was in a nominally post-evangelical mood not just to revisit pre-“Slow Train” items from his catalog (an acoustic/Americana “To Ramona”) but traditionals (a thoroughly electrified and rocking “Jesus Met the Woman at the Well”), oldies old and not-quite-as-old (“Fever,” “Sweet Caroline”) and even recent AM/FM soft-rock chestnuts (Dave Mason’s “We Just Disagree”). It’s as if he’s rediscovered non-Jesus Music in such a big way that his appetite is boundless, hitting on Tin Pan Alley, folk and Mellow Gold with the voraciousness of, well, a convert. He didn’t just want to sing his old songs again, after denying them during his “Slow Train” tour — he wanted to sing everybody’s old songs.

Other delightful covers are scattered throughout the “Shot of Love” and “Infidels” years — a version of Frank Sinatra’s “This Was My Love” that prefigured the series of all-Sinatra albums he would come to record in the 2010s; one of Willie Nelson’s greatest and most under-heralded songs, the romantically magnanimous “Angel Flying Too Close to the Ground”; the country fatalism of “Green, Green Grass of Home” (by Curly Putnam, who later used a variation on the same deathly twist in “He Stopped Loving Her Today”); visitations with Elvis, Hank and the Everly Brothers; and maybe the single most blistering track out of the 57 included here, a duet of the blues standard “Baby What You Want Me to Do” with his favorite singing partner, Clydie King, that finds beauty in a plunge into pure rock ‘n’ roll distortion.

Of the original songs that didn’t make it onto Dylan albums contemporaneously, some have already been released in other takes in previous “Bootlegs” — like, obviously, the holy grails “Blind Willie McTell” and “Angelina” — and some were covered by other artists before he got around to belatedly releasing his own versions. It’s grand to finally, officially have his own version of “Let’s Keep It Between Us,” even if its pleasingly bizarre chordal twistiness found its ultimate fulfillment in a superior cover by Bonnie Raitt; there’s little doubt that a plea to a lover to keep things on the down-low to avoid gossip sounds especially meaningful coming out of the mouth of as lifelong a publicity avoider as Bob Dylan. The Williams Brothers probably did “Straight A’s in Love” in their Everly-esque fashion even better than Dylan’s rave-up here, but how charming it is to hear the bard at his roots-rock goofiest. Likewise, Carla Olson and the Textones might have had a fiercer take on the protest song “Clean Cut Kid” than Dylan did by the time he released one himself, but it’s fun to hear it transform in the different variations on this set, from a more straightforward roadhouse tune to a nearly finished version with nearly comical female backup vocals added for gallows irony. “Lord Protect My Child” may really belong to Susan Tedeschi at this point — but “Infidels” would have been all the better for it if it’d been included and been made to firmly belong to its writer at the time. When B.B. King covered “Fur Slippers,” the most in-the-pocket straight blues song Dylan ever wrote, it seemed like something out of the 1940s Delta, not Dylan’s back pages.

Lesser known to all but the truly bootleg-conscious are cuts range from “Tell Me,” a light-hearted, samba-inflected ballad that sounds like Dylan covering something out of the Dean Martin catalog, before the lyrics grow weirder and give it away as a Dylan original, to “Julius and Ethel,” a barnstorming song about the Rosenbergs that indicates just how much of a return to protest music “Infidels” would have seemed if this had been put on that album alongside “Neighborhood Bully” and “Union Sundown.” Multiple variations on the previously “Bootleg”ed “Foot of Pride” trace its development from a very different, equally good song that was first called “Too Late,” available here in both solo and band versions, either one of which would have raised the stakes for “Infidels” higher, too.

Among the alternate takes or mixes that outdo the officially released versions, “Lenny Bruce Is Dead” is heard with a stately, minimal string arrangement that incalculably elevates what otherwise was arguably the dodgiest track on “Shot of Love.” “Death Is Not the End,” which got held back for release in edited form on a later album, plays out much longer and much more powerfully here — if it’d been released as the final track on “Infidels,” we might be calling that album a masterpiece instead of very good. “Neighborhood Bully,” his cleverly crafted (whatever you think of the actual politics) defense of Israel, benefits from a slash-and-burn three-guitar attack that in this rawer mix cuts even closer to the bone. “Don’t Fall Apart on Me Tonight” gets two different readings, both better than what was heard on “Infidels,” and one of them tender enough to really deliver the idea that Dylan’s the one in danger of falling apart. But maybe no song benefits quite as much from a different arrangement — and, in this case, a markedly different key — than “Empire Burlesque’s” “When the Night Comes Falling From the Sky.” The original album version is a sonic travesty, although you can see where Dylan and the maligned Baker were headed in their use of minor chords to fashion a dramatic title into a more melodramatic song. The two major-key renditions included in this set feel like classic Dylan, though — especially the faster one that brings in Steven Van Zandt and Roy Bittan to turn the song into something like Dylan appropriating the E Street Band to sound like Springsteen himself at his Dylan-imitating best.

If there’s a major complaint to be made about this boxed set, it’s in the lack of live material that’s been a staple of so many other “Bootleg Series” releases — although it should be noted that the “gospel years” box that had some overlap with this era, “Trouble No More,” did include an excellent full concert. The dearth of that here comes to the fore when two completely blazing live tracks are tacked on to the beginning of the final disc: “Enough is Enough,” a rocker that he apparently only ever played a handful of times live, never properly tracked in the studio; and a beyond-garage-rock version of “Infidels'” “License to Kill” that Dylan did on David Letterman’s late-night show with L.A.’s punky the Plugz as a stunning choice of backup band. The effectiveness of his backing unit on these two live tracks, or of his “Shot of Love”-era group on the rehearsal tracks on disc 1, point up that maybe things were getting a little too tame for their own good on the “Infidels” album, as remarkable and generally well-arranged as it was. These were maybe some of the the last years in which Dylan was looking for tact, good taste or certainly any sense of commerciality in the players and producers he chose to use; the “Never-Ending Tour” would get underway soon enough, and he and his bands have hardly stopped swinging since.

This hardly begins to get at all the rich topics of discussion raised by the set — like, is the 11-minutes Sam Shepard co-wrote “New Danville Girl,” later to be refashioned and released as “Brownsville Girl,” one of Dylan’s greatest epics or one of his most insufferable, or a little bit of both? Let’s leave that Pandora’s box of debate closed for now and agree, if we can, that “Springtime” is one of the fall’s essential boxed sets, in a season that’s already had an embarrassment of riches for archivally minded physical-media buffs. It’s less akin to the sets celebrating George Harrison’s “All Things Must Pass” or the Beatles’ “Let It Be” than it is to the Beach Boys’ recently released “Feel Flows: The Sunflower & Surf’s Up Sessions 1969-1971,” another expansive set that sticks up for a time in which a great rock act was working erratically and yet at least partly in his or their prime.

It’s certainly a corrective, anyway, to the misconception that he jumped from a hardcore Christian period to a wanna-be MTV-relevant period without much greatness to show for the gear-shifting. To anyone who still thinks that: Unbutton your shirt, relax and stay a while.