The flowers are etched but as far as cut or pressed I look for any faint lines that would indicate mold marks rather than sharp vs not sharp. Some manufacturers worked the edges of cut glass so that they would not be sharp. Some manufacturers did the opposite for pressed glass. While it was a recent piece, Macy's, I cut my finger on a pressed piece when I slid my finger.

Pretty. I would guess (and it's hard to tell from photos of course) cut glass. Does it feel heavier than it ought to? That would suggest leaded glass which would be the stuff used for cut glass. Feels like a brick and tinkles like a bell :P

Get a closer photo of the hatchmarks or the flowers (they look like they might be cut and not etched but that could be an artifact of the image).

that's pressed with "wheel etching" done with a wheel like "saw" thingey as opposed to acid etching.
Mold marks have nothing to do with cut or pressed, and heavy weight doesn't either. there are lots of old pressed patterns made in lead/flint glass.
BUT....there are a lot of pieces of glass made not too long ago ( like from 1960...grin) that are a combination of pressed and cut. The basic pattern is pressed but certain elements of decoration are cut. Usually made in Czech/Bohemian countries. I think that's what your piece is.

Not from the 1960s, that's for sure. All the cut/pressed glass I have is from the collection of my stepmother's mother, who died in the 1930s. She was a Scottish immigrant who loved American cut glass.

The compote feels heavy to me, but what do I know? It's small--only 6" in diameter, and 5" tall--and weighs a little over 1.5 lbs.. I tapped a crystal goblet against non-crystal glass, and it made a pretty ring. Then I tapped it against the compote, and the ring was outstanding.

As I said.....because it has good lead content to the glass doesn't mean it isn't a pressed design. The flowers on your piece are wheel etched....can't see well enough to know if the rest of the design is cut, but the base is definitely formed in a mold.
And prehaps there was pressed glass that was enhanced by cutting some of the design earlier than 1960....but those pieces are the ones I am familiar with.
Have you looked closely for a mark?

I don't see a mark anywhere, but when running my finger around the bottom of the base I discovered a shallow chip and several slightly raised lines that I assume could be mold marks. Well, it's not terribly important. I don't plan to do anything with any of the glass. I sell stuff on eBay, but avoid anything this breakable. I just like to keep a record of information on various objects and pieces of furniture so my kids know what they've got someday.

Many thanks for your input!