babbie, Just FYI - I have also seen the slide-out low-profile hoods by KitchenAid and Broan. Donna

It's a universal recommendation that the hood be at least 6" wider than the surface it covers. And as deep as you can manage. It has nothing to do with the fuel used to heat the food. It has to do with the fact that smoke, steam, smells, and aerosolized grease particles rise upwards and outwards. That's physics. A smaller hood can't capture all of those yucks. Stronger fans can't compensate for a lack of capture area either. It's more important to have a good capture area than a strong fan.

Take a look at VentAHood from Richardson TX. Dealers nationwide. Their PRH6 line is 6" tall and they have 36" widths. Here's one: https://ventahood.com/index.php/products/application/under-cabinet?id=360&model=PRH6-K

There is a thread on here about the VaH ARS system. I think it is here (from notes -- not checked):: https://www.houzz.com/discussions/2347276/vent-a-hood-ductless-ars-range-hood-update#n=65 Opening a single window will spread the grease around just as well or better than a recirculating hood that is crippled with no or slight filtering. Opening one window and using a large window fan in a transverse window (with the cooktop in between) might be better than a non-performing recirculating hood. Please reread my comment. Any hood used has to have adequate performance or it is a waste of money. " Shelly Miller, PhD, a mechanical engineering professor at University of Colorado Boulder, told us that if you don’t have an exhaust hood over the stove that vents directly outside, you’re better off opening a window or running an air purifier." I don't know the date of this telling, but it should be obvious that a grease filter will reduce the amount of grease recirculated, and a charcoal filter (also part of the ARS) will reduce odor. An air purifier that could filter at a 300 CFM rate would be quite the beast; at least the same scale as the ARS. If the filter takes seemingly forever due to its low flow rate, then filtering works mainly by letting the grease aerosol particles settle out on the surfaces and fabrics. Absolutely the recirculating design needs mesh or baffle filters (mesh may be better at low air speeds) or the VaH approach of centrifugal impingement using the blower -- and -- charcoal filters for odor removal. Serious grease particle removal might require stacks of different filter devices. These are available for commercial purposes. [all I have time for this morning]