Back when Tim Curry was a kind-of in demand recording artist, he made two albums of original material–and then released a “Greatest Hits” album. I think Julie Brown did something similar, except all three of her albums had mostly the same six songs on them (One was her first album, the second was a movie soundtrack, and the third was “Greatest Hits.”) I think “Greatest Hits” albums are a contractual requirement after X number of years without new material, but I could be mistaken. Anyway, are there any examples of an artist whose second album was actually called “Greatest Hits”?
Smash Hits by the Jimi Hendrix Experience was released after two studio albums, in the UK. In the US it was after the third album.
Mass Slaughter: The Best of Slaughter was released after their second album.
Incidently, while looking up some bands I discovered that trivia that the first Greatest Hits album was Johnny’s Greatest Hits by Johnny Mathis, released in 1958.
I’ve never heard of such a contract provision after 50 years of reading about rock, but there maybe could have been one. Hard to imagine that any record company would promise that to a new group, and any company resigning a known group would want new material and maybe not even have the rights to the older stuff. Much more usually, they are rushed in to cash in on sudden success, or fill in a gap in recording, or used to fulfill a commitment to a company the group wants to get away from.
Way back in the 60s, greatest hits albums were done early in careers, because rock still focused on singles, so putting out a collection of hits just meant all the singles in one place. The Byrds did one after four albums and Buffalo Springfield after three.
So Far was the greatest hits album for Crosby, Stills, Nash & Young and released after their first two albums. Still went to #1.
How about the first album?
Take Mrs. MIller, for example.
Her first album was called Mrs. Miller’s Greatest Hits.
There was also the punk band, The Cockney Rejects.
Their first album was called Greatest Hits Vol. 1. Their second album was called Greatest Hits Vol. II. (Yes, they changed to a Roman numeral the second time.) Their third album was… Can you guess its name? It was called The Power and the Glory. They actually released 8 new albums after the first two that had more original names.
To make things even more confusing, the same year they released The Power and the Glory, they also released an album called Greatest Hits Vol. 3 (Live & Loud), which not only dropped the Roman numeral usage, but was an actual compilation album of previous hits. And they ended up releasing a total of 9 compilation albums, including at one point Greatest Hits Volume 4: Here They Come Again, 20 years after the release of their debut album. There was also an album called The Best Of The Cockney Rejects at some point.
I guess when you are a punk band, you don’t have to make sense and you can just call things whatever you want. (Also, the Cockney Rejects were a pretty influential band; their song “Oi, Oi, Oi” spawned an entire musical genre called simply, “Oi!”)
It seems that it’s not really that odd for a debut album to be called “greatest hits” for a music act. There are some other examples I could dig up. The reason for this is that sometimes the debut album is a compilation of previously-released singles, so they really are hits already.
I recently read that Men At Work released three studio albums and eight greatest hits compilations (so far!)
I’ve never heard of such a contract provision after 50 years of reading about rock, but there maybe could have been one. Hard to imagine that any record company would promise that to a new group, and any company resigning a known group would want new material and maybe not even have the rights to the older stuff. Much more usually, they are rushed in to cash in on sudden success, or fill in a gap in recording, or used to fulfill a commitment to a company the group wants to get away from.
I got this impression from reading about Michelle Shocked (I like her, but you don’t have to) putting out a greatest hits album called Mercury Poise, a contractually obligated album she had to crank out to malicously comply with her contract with Mercury Records, which she was trying to separate from at the time. The goodbye album might not have had to be a GH, but that’s likely the fastest way to get past such an obligation.
I recently read that Men At Work released three studio albums and eight greatest hits compilations (so far!)
I think it’s more like three studio albums, three compilations, three live albums, and three EPs, but yeah, that’s excessive!
The German punk/new wave band Extrabreit pulled a similar stunt and called their first album “Ihre größten Erfolge” (Their Greatest Successes), being totally unknown and never having had a hit. Ironically, it became a big hit.
Buffalo Springfield only made three albums before disbanding. So that would have been the time.
The band that immediately came to my mind was Edison Lighthouse of “Love Grows (Where My Rosemary Goes)” fame. In an age of singles, they released one studio album in 1971, one in 1977, and then 11 “compilation albums.” There was also a “live” album released in 2003.
To the best of my research, they released 8 singles in total, but only 2 of them made the charts at all. There are 14 albums based on one lonely top-40 single.
A lot is explained by Tony Burrows’ involvement.
Are you not describing the third album being a greatest hits album, not the second? Because presumably a greatest hits album as a second album would just be a repeat of the first album, or a reduced version. At least the third album can combine the most popular songs from the first two.
There are cases when a band releases non-album singles before and during they release their first album, and those singles with the outstanding tracks from the debut album land on a Greatest Hits album. Sorry, I can’t come up with an example, but I’m sure there are some.
I did a bit more research. Their second album, titled Love Grows (1977), “is a reissued compilation album/EP distributed on the SMA label in the UK.” While it’s not titled “Greatest Hits,” it appears to have no new tracks that weren’t on the first album or released as singles. Therefore, I think it qualifies under the OP.
All the remaining albums were issued at least 15 years later.
Their debut album (1971), was titled “Already.” This almost suggests that it was intended to be a collection of their hit singles to date.
Darn! Looks like at least two tracks on Love Grows were not previously released as singles or included on their first album.
If you only count LPs and not EPs, Bow Wow Wow released a greatest hits in between their first and second LPs.
"I Want Candy
Following the success of the “I Want Candy” music video on MTV, RCA compiled an album, I Want Candy, to capitalize on their newfound American audience. Once again, the cover photo (by Jim Varriale) featured a nude Lwin painted entirely in gold. Side one of I Want Candy contained all four tracks from The Last of the Mohicans and “Baby, Oh No”. Side two consisted of four tracks from See Jungle! See Jungle! Go Join Your Gang, Yeah. City All Over! Go Ape Crazy! and “El Boss Dicho”, the B-side to “Go Wild in the Country”. The album peaked at No. 123 on the Billboard 200.
Meanwhile, EMI reissued all their recordings under the same title I Want Candy. The EMI album matched *See Jungle’*s position of number 26 on the UK album charts. It was released in North America as Twelve Original Recordings and elsewhere as Original Recordings."
As an aside to the OP, how many “Greatest Hits” albums do the Stones have? 15? 
A lot.
And what do you do in cases where the artist’s legitimate Greatest hits album is their best overall album? Like the Eagles, or the Doobie Brothers?
Don’t forget Pete Best’s first album, Best of the Beatles 
The very first greatest hits album (Johnny’s Greatest Hits - 1958) included a previously unreleased track, so that shouldn’t be a blocker.
Thank you, Telemark. I was trying to decide how to properly express my shame.
Look at band’s discographies on Wikipedia if you want to see corporate exploitation at its finest.
The Stones list 28 compilation albums, a group that includes some UK or US only releases, rarities, b-sides and other non-hit stuff. The Beatles have 50, with many more individual country releases, and that doesn’t include five from their pre-fame work. Every other major performer or group shows the same pattern.
Paul Simon once wrote “every generation throws a hero up the pop charts”, but record companies know that every generation wants to buy older heroes as they get introduced to them. A never-ending double/triple/extuple dipping into the pool of money.