Quoting:
I'm trying to find some CDs.  I really like Dream Academy.  I remember way back in the 80s I used to listen to them all the time when I would cassette tapes.  Over the years, I lost them.  Now I want to get it on CD.  

Anyway, can you think of a band that you REALLY liked but they never got much airplay?  
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The first Dream Academy record is still one of my favorite '80s relics.  Very pretty, sweet, and precious, but maintains substantial songwriting throughout.  Kate St. John went on to work with Roger Eno (Brian Eno's little brother), the best thing they did together was a 1992 album called "The Familiar" (All Saints).  A couple of years later, KSJ released a solo CD on the All Saints label.
Killing Joke were never stadium sell-out huge, but they've been putting out music for nearly 25 years and have a very respectable international following.  Their latest album, eponymously titled, was released last summer.

Others I'd recommend from my side of tastes:
Blancmange
Wire Train
The Chameleons UK
Bill Nelson
Strawberry Switchblade
Fiction Factory
Wall of Voodoo
B-Movie

Quoting:
China Crisis
Spandau Ballet (in the US)
Kix
Scritti Politti
Fun Boy Three (in the US)

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Spandau Ballet had a HUGE in the US with "True."  It's an easy-listening favorite to this day.  "Gold" also went top 30.  Scritti was fairly well-known.  "Wood Beez..." and "Boom! There She Was," were both alternative and dance chart hits, but he never broke REALLY big.
Fun Boy Three's version of "Our Lips Are Sealed" got respectable US airplay, but that was about it.  My favorite FBT song is "Farmyard Connection."

Quoting:
Do you guys remember bands like Blue-Mercedes;  Dream Academy; Glass Tiger;  Bourgeois Tagg; The Wonder Stuff; Kitchens of Distinction; Killing Joke; etc...?
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I remember Dream Academy - Life in a Northern Town plus they had a few songs on Ferris Bueller's Day Off - a remake of Please, Please, Please Let Me Get What I Want and Edge of Forever. Bourgeois Tagg with Mutual Surrender and I Don't Mind at All.  Great songs. Glass Tiger was recently or is on tour w/Platinum Blonde in Canada. Go to Amazon.com and see their selection of Dream Academy CDs. Some used if you prefer. I really liked The Church but didn't hear as much as I wanted to of them.

Quoting:
One name that comes to mind is Honeymoon Suite - they had one Top 40 hit in 1984 with "Feel it Again"
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Actually, where I lived at the time Honeymoon Suite (they were just here in Vancouver, BC on Valentines Day) was very popular and many of their songs were played.

I was always frustrated that the local FM stations didn't play enough of Marillion and Missing Persons and Queen City Kids.  :(