I think I would just say you have big soffits!

Look in the hvac to see what is lurking in the soffits and consider getting rid of all or part of the soffit. The ac vent could be routed under the kitchen for better air flow (unless that is a return duct).

Most likely electrical and plumbing is hiding up there also, so have to decide cost vs function benefits. We took down our ceiling, moved the ducts(much better air flow now),moved 3 plumbing runs and some minimal electrical. No more soffits and even DH , who wanted to keep the soffits loves the new look!

Soffits

No soffits

Usual iPad cryptic and completion matching errors...

I think the word you want is troffer, which Merriam-Webster defines as "an inverted trough serving as a support and reflector usually for a fluorescent lighting unit. Origin of TROFFER. blend of trough and coffer." This type of fixture is used more often in commercial settings, and you'll hear the term in that setting.

I don't have any great suggestions on what to do with it aesthetically, but you could look at commercial installations for ideas. However, if the lamps are T-12s (that is, if they are 1.5 inches in diameter), you can save energy by replacing them with T-8s (1 inch in diameter) and still get the same light output. I think you'd need to replace the ballast as well.

Or you could go LED with this fixture (see below). Cree has a good reputation on the board for its LED recessed cans, and the fixture I linked to has an excellent color rendering index (CRI=90), and comes in various color temperatures.

The commercial fixtures do have a bit of an institutional look, though. I like Annie's suggestion for a bit softer effect.

Here is a link that might be useful: Cree CR24 2'x4' Architectural LED Troffer

I guess it depends on the extent of any reno you are doing what your options are. a2gemini's suggestion is great if you are doing a large reno. On the other hand, I've seen what Annie suggests done and thought it looked very nice and for far less investment of time and $. I've also seen that done with 4 recessed cans added to the inset area for great light rather than any type of ceiling light fixture. Sometimes the area is painted as an accent to draw attention to it as an interesting architectural detail if crown moulding isn't used. Good luck.

I like what Annie did also. But getting rid of the soffits was not as bad as I thought- the major extra cost was taller cabinets...
Lots of options to explore!

I could be wrong, but I don't think those are soffits. I think the box is actually recessed, framed in among ceiling joists. If so, a2gemini's idea won't work (or would be a very expensive structural change, anyway). Looking in the attic should answer that question pretty easily.

If I'm wrong, though, and a2gemini is right about the structure, eliminating the soffits is a great option.

I've also heard them called a light box. They were pretty common in the 70's - our house has them in most bathrooms, the master bedroom closet and the kitchen. They aren't popular right now, but we preferred the amount of light it gives out and appearance to the many holes we would need for recessed lights to get the light we want in the kitchen. Ours goes well with our kitchen's transitional lines, IMO.

Ours is as cawaps described. A box framed by ceiling joists. It's twice as wide as the space between a pair of joists so their are sistered joists on either side of the box to take the load of a joist that ends in the side of the box. It would be a major structural change to raise the ceiling to the height of the top of the box because all the joists would have to change. These are not extended soffits. (Our old kitchen had soffits at the top of the old cabinets which we removed.)

Ours has a minimal metal frame around the box and dividing it into sections and plastic panels to diffuse the light. DH replaced the ballasts and fixtures in the box with ones that take newer fluorescent bulbs. I think he said that the older 70's bulbs were being phased out and the new bulbs and ballasts were better. We have 5 pairs of bulbs but with the old fixtures we had more.

Hi everyone,
Thank you for all the comments and suggestions! The box isn't soffits - the upper cabinets are 42" and run to the ceiling. The box is as cawaps and cloud_swift describe - it goes into the attic space between the ceiling joists. I'd love to have the entire ceiling raised to match the box, but that would mean literally redoing the entire roof support structure.

AnnieD: that is a lovely suggestion with the rope lighting behind the crown, and a fixture in the middle. I had contemplated can lights but I wasn't sure I would get adequate area illumination.

Whatever I end up doing, I'll post a before and after.

I saw a ceiling yesterday that had something similar (new construction though) with crown around the top of the recessed part as well as around the edge of the opening. The wall in between was painted blue and I'm trying to remember the wall and ceiling oolors. It was my dad's realtor's office -- I could go by and take a picture. A semi flush or chandelier that hangs down just enough to peek out from the opening (either all or in part-- depending on the fixture) would be nice. I don't think a flush mount would do it, but again, might depend on the fixture.

Fallingwater's living room (image from Flohaus.com) has a shoji=like panel in it's troffer:

Lascatx, the crown in both places sounds like a good idea; you also mentioned a blue paint. I was thinking about painting the inside of the box a light blue (SW Atmospheric, to match my porch ceiling visible from the kitchen window.)

Palimpsest, Fallingwater is always a gorgeous inspiration! More things to contemplate, certainly!

I couldn't see Annie's picture earlier, but it is there now. What I saw was similar, but with a stained crown at both levels, and there was enough depth to see the upper one back in the corner. You might want to get some pieces of trim to play with and make sure you would be able to see both levels and get the full effect.

we're taking down the covers, removing the fluorescent fixtures and replacing with faux beams that will house recessed can lights.