I don't have a specific recommendation for you, but I do suggest you read through this forum, or do a search in the search box at the bottom of the Appliances page (search "quiet hood" or something like that), there are a lot of threads on this topic, and the hood selection is vast.

I just wanted to say that a great deal of noise in a hood arises from the ductwork. If the duct diameter is too narrow, typically less than 8", then the exhaust will be noisier. Also, if there are a lot of bends in the exhaust ductwork out of the house, there is a lot of noise. And if the duct run is very long, that creates a lot of noise. That is why you can have two identical hoods in two different homes sound very different, due to different ductwork. Many times people blame the hood for noise, when the duct is to blame. Also, know that ANY motor, at head height the way a hood is, will be noisy. People get around that by having inline blowers or external blowers, but they are more expensive.

You should try to get a hood with baffle filters, rather than mesh filters. Baffle filters are quieter, more efficient, last longer, and need cleaning less frequently. E.g. you would never find mesh filters in a hood in a restaurant, only baffle filters.

As to CFMs, the rough rule of thumb is that for every 100 btu's in your burners, you need 10 cfms. So if you have 4 burners with each one 15,000 btu's (total of 60,000 btu's), you should have a 600 cfm hood. Do not shortchange on the cfms. There is no point is spending money on a hood if it is inadequate; you would then be throwing your money away. In your OP, you said you "don't need a lot of cfm's". Some people feel 600 cfms is really low, others feel 1000 cfms is really low. So, can you be more specific about how many btu's your burners have?

Not sure which of your posts to respond to, but since AK started here I'll continue. Two quotes from you:

"I don't need a lot of CFMs."

"Here is the set-up in my house: stove, a window immediately above that (about 20" top to bottom), then, about 12" above the window, a duct for a fan (or hood?). The duct vents directly out the wall and used to contain a fan. Immediately above the 8" round duct is the ceiling (and I mean "immediately"--there is about 1 mm of space between the top of the outlet and the ceiling). This is why I am hoping I can somehow convert an under-cabinet range hood."

Starting with the first, let me just say, "I believe you." People are CFM crazy around here, leaving you to think that if you can't sear a fish in a screaming hot cast iron pan without smelling it ten feet away, you've got inadequate ventilation. But if you're like 99% of the rest of the country, chances are you just want to exhaust a certain amount of steam and odor, and you rarely cook something that's overly offensive in either odor, grease or smoke. Like all those people who do just fine with a recirculating OTR microwave whose fan they never turn on.

If I'm right, and if I'm also right in that you have no desire to close off that window above your range, then here's one suggestion based on how I'm interpreting your second quote: Build a "box" hanging down from your ceiling as low as you can go with it being aesthetically ok, then install an inexpensive power pack or insert or whatever you want to call it as high as possible. With this you will have maximum capture area and your motor will be as far as possible from your ears. Don't worry about baffle versus filters. I can tell you from first-hand experience that at least at CFM levels up to 360, you won't even be able to tell the difference in noise between a mesh filter in place and running wide open with filter removed.

Since noise is one of your primary concerns, my number one suggestion would be to find one with infinite speed control versus three or four speeds or whatever.

Many will probably disagree with me here. But I think that if you do a search on this forum, as AK suggests, you'll also see that people here are way more fanatical about ventilation than the average person. Can't hurt to read it all though so you can make your own informed decision.

Ditto.

One correction: an inline or esternal blower can be good and low price too.
I got an inline 300 CFM blower for less than $150. From a fantech distributor( but not from the first one I contacted). It's an FG-6. It's quiet. I built all the rest.

HI. Thanks for the replies. I have an old GE gas stove, about 9600 btu per burner, and I usually have only one or two on at a time.

The blower idea is a possiblity. Thanks for that thought.

Do you think I could install an under-cabinet range hood with the set-up I have?

I have looked through the forums more thoroughly. My budget is quite tight, so I am trying to get a very good range hood inexpensively on ebay.

Because domestic and commercial kitchens have varying layouts, there are a number of range hood types for different situations and setups. Additionally, range hoods use different operating principles to filter kitchen air, with certain designs more suited to domestic over commercial uses, and vice versa.

Here is a link that might be useful: range hoods

I think Sarah Simonsen is a spammer. New to Houzz and posted this same link in 4 threads. And the linked website is full of hooey.