Are they called Speed Ovens these days? Or is that something different?

I had a model by Sharp for many years. When it died, I got a model by GE. Both are/were countertop units. Finding something shallow might take a little searching. There's also no reason why you couldn't use an OTR unit, just don't connect the venting.

Speed ovens are usually a bit more flexible, giving you combinations of microwave and heat at the same time. My Sharp only had two fixed settings. The GE has only one microwave power (around 30%) but allows you to change the temperature (max around 450F).

A speed oven sounds like overkill for your needs, and a waste of money if you don't need one. There are some microwaves (I don't know if they also have convection oven settings) that are meant to install under the upper cabinets, just like you want. They don't have the sad fan that over the range units have, but are very similar if not the same otherwise. I think GE has one. You might have to page through some product listings to find it.

If you prefer a unit that doesn't come that way, you can build a hanging shelf for a countertop model, however you must limit the height. Even so, the counter space under any unit isn't going to be all that useful. It may be possible to modify the cabinet so that the microwave can sit a bit higher.

IF I can find one, I will probably install a shorter cabinet. At least a deeper cabinet. Right now my upper is only 12" deep, but I use the bottom shelf for a small microwave currently. If I can find what I am looking for I will definitely get at least a 15" deep upper cabinet and either build it in on the bottom or get a short cabinet and mount it under.

I am trying to keep from having to buy a new double oven stove (another long search process). It's either this or $3000. I'd rather not spend $3000 if I don't have to.

We have a GE Profile countertop convection microwave, and although ours is about 10 years old, I just googled and it appears to still be available (more modern version) for about $700. I got it for the same reason you mentioned, only one oven otherwise. However, I have never needed to use the convection setting in all this time. We actually have it on the bottom shelf of an upper cabinet, but it just sits on the shelf (not built in). Good luck!

If any of you have model numbers, that would be appreciated.

Joe

to help with those times when I need a second oven. This would really be just a second oven, like during Thanksgiving or other big meals when cooking two things at once comes in handy

This shouts to me one of the Breville counter oven models, not a MW. My experience with a MW trying to double as a regular oven is that they do such a poor job at being a regular oven, it's a waste of money. The only problem is your lack of counterspace. The Breville "Smart Ovens" come in 3 sizes. The smallest would work even with limited counterspace. Though IMHO, if you are going to go for a second adjunct oven that is truly useful, I'd get the Breville middle size, it's just right. Look on Amazon for good prices, and also if you get the coupons in the mail from Bed Bath & Beyond, you might find good prices there.

My experience with a MW trying to double as a regular oven is that they do such a poor job at being a regular oven, it's a waste of money.

To be fair, I know two or three people who have the older model GE OTR convection micro and they use it all the time for baking/roasting and like it. But they have made substantial changes in the current model and the reviews on that are not so glowing. But I agree that a Breville would be great if you can figure out where to put it.

I needed to replace a countertop microwave that we just used for warming/melting/defrosting and I hated the idea of eating up that counter space for such limited use. I ended up getting a Samsung Convection Microwave. Been using it for six months and it works as it should for its microwave functions, but I am also using it as a stand-in (small) oven instead of firing up my big 30" ovens for small tasks.

Works great for roasting small amounts of veggies, heating chicken nuggets, reheating a few slices of pizza on a small stone. My daughter even bakes muffins and cupcakes in it. It also will dual microwave and convection when you are trying to (i guess) speed cook.

http://www.samsung.com/us/home-appliances/microwaves/countertop/mc12j8035ct-1-2-cu-ft-counter-top-convection-microwave-with-power-convection-powergrill-duo-black-mc12j8035ct-aa/

This particular model fits well for my location because its taller than wide and the door opens down rather than swings. Even though its footprint is a little bigger than the Sharp it replaces, it 'uses' less counter space.