Can anyone here recommend a lathe for doing cartridge brass modifications, turning rims off rimmed cases and cutting extractor grooves? I don't want to tie up bench space with the lathes I see on the market. Hobby lathes seem too large for turning small pieces of soft cartridge brass. I've always heard of jeweler's lathes, but don't know a source or reputable brand.

I have never used one having resorted to chucking brass in a drill using a plastic brush and rotating the rim on a file.
A quick search yielded several hits on FleaBay and these:
Unimat SL1000 Watchmakers Lathe For Sale (Menasha) | Esslinger Watchmaker Supplies Blog
Jake's Pens
Even the well used ones are going for most of a $1K.
Neat toy certainly though.

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NEMO
"Everything 44"

Sherline lathes are pretty good. See: Home - Sherline Products

I bought one used, and fairly well equipped for about $200 around 15 years ago and use it for lots of things, including cartridge case conversions removing rims, cutting extractor grooves, thinning rims, etc.. It works well, and I have added quite a few accessories over the years. I also have the conversion used to make it into a small milling machine, which I have not used a great deal but it works OK. My B-I-L has a fairly complete Sherline outfit he bought new, and uses it all the time for various hobby projects. He is also sort of an inventor. You might see what's listed on eBay.

I actually just bought a grizzly G0745. It's a 4x6 so not too big. There are nicer ones to be had but this is working fine for turning brass. Weighs about 30 lbs. I have also turned a couple of steel mandrels for turning the cases on and it seems to have enough power so thumbs up so far. It's light enough I can take it off the bench and stow it on a shelf when not in use.

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Trucks and guns.

You've gotten some good advice from some people that know more about the subject than I do. I can only suggest getting something for which parts and tooling are available. I had a nice 6" Atlas backgeared lathe for about 30 years that had been used for 20 years to turn armatures in a generator/starter shop. It was in great shape but parts were becoming harder to find and it was too big (bench space) for things like cartridge conversions and way too small for whatever the next project was that I wanted to build. Unfortunately I had to sell it when we moved to a place with a smaller garage/workspace.

As much as I would like to buy American products I buy one of the Grizzly hobby lathes to do cartridge conversions, etc. An old industrial arts teacher that I used to shoot with had a Sherline that he found in a yard sale. He used if for a while to make various little odds & ends but got a Grizzly and liked it.

Search for a 4" Sears/ atlas lathe. These can be found used.

Doing lathe work on cartridge case conversions is very elementary and does not require a high degree of precision and versatility. Virtually any basic small lathe will be more than adequate for that purpose. As I said earlier, my Sherline works fine for that application, and takes up little space, but I would go with whatever I could find the cheapest that I had space in my workshop for. I think Sears used to sell Sherline lathes under the Sears name, but I doubt if they still do.

Smithy is another company that imports Chinese machines. I do have one that runs many jobs on auto parts that I fab for older cars I own.

I have a Unimat and also a small Sears Atlas. The Sears has a bit more power than the Unmet...but it IS older. Unimat is going to go to a new zip code one day soon.