Well, after this thread came back to life last month, I went back to shopping online for more 3" CDs.
One lot I bought on eBay had several promotional releases from Europe in the late 90s. Both of these were from the Echo Label in the UK from 1998. Having an inner cardboard sleeve in an outer slipcase gave them more space for promotional copy and images.
[Edit]: after posting this earlier today, I learned that
Jóhann Jóhannsson of LHOOQ has passed away today.
Similar idea with this triple panel gatefold with a "belly band", released on Electric Canyon in 1999.
And now the real oddball. The listing said something about this CD not being compatible with all players, but didn't explain why. This EMI 1999 release was in a gatefold sleeve, about a half-inch taller and wider than the normal 3" CD sleeve.
The back has two stickers, including the warning.
Once I got the CD out, I made the discovery that this "disc" is square.
I also got several more of the Rhino Li'l Bit o Gold oldies series, and another from the Absalom 3"CD series with the letterpress sleeves, a noise-hip-hop EP by Soul-Jazz.