It's called a Padded Half-Cup normally, but this is really a Demi since it covers above the apex by about 1.5", more or less depending on size but the apex is clearly visible if you look at the cups from the side when not worn. Demi is cut straight across for a more corset look in that it showcases the upper bust, whereas a half-cup is just that, not an everday bra because there usually is no nipple coverage. Also...this thing is not padded. The ever so thin lining is almost like a super thin quilt batting. It's about 1/16" thick at most and if you compress it between your fingers it's as thin as two layers of thin fabric put together - and with a correct fitting cup your boobs actually compress the fabric. When it's too loose there is no compression and the bra will stick out more. If you're getting a size boost from this, or any lined bra for that matter, then your cup is too large.
Something else to note: Demi bras are better suited to shallower breasts, so if you're fuller on top or you have a bit of volume these are not going to fit you. Some websites say these are suited for A-B cups...if you're familiar with Freya they barely have any bras starting in C, nevermind B. This is a shape specific style, NOT size!
Update 2/04/13: Booo...this no longer fits good! I could really go up a cup size and as of now am no longer suited to Demi's because of remigration =( The only thing that could possibly fix this now is if I can manage to find longer and very narrow wires so it changes the shape of the cup some. Same goes for the Daphne.
I also, finally, put a dart in the center gore of my Panache Cleo Sadie....waaaaaaayyyy better fit. I've done this to bras in the past, some it works with, others it doesn't. This bra was a good one for it because of the way it's constructed and the shape of the cups. Normally the vertical seams kind of point away towards the sides and then in / \ kind of like that. I took off about 1" of the band with the dart and now the seams point more like this \ /, though slightly straighter, so it gives better lift and support from the bottom of the cup rather than just smooshing you down.
Mods I have left to do for underwear include taking in the band or at least minimizing the stretch in the Freya Edina Longline, turning the Panache Cleo Jude from a partial band plunge to a full band balconette/plunge, taking in the band and center gore of the Panache Porcelain (this one I have in 30F because 28F didn't fit and I thought at the time 30 would be the sollution when I should have gone for 28FF), and I may also turn that bra into a full band style...I haven't decided yet. I still have a thong to make for the Fantasie Bridgette Basque turned Longline too.