Thanks so much, @Sabrina Alfin Interiors! I hadn't thought of sheers! You are correct, I don't need them for privacy. The only functional need is that the sun comes through one window in a blinding way at a certain time of year, around the time I eat breakfast, so I need something that covers the top half as well. I see from the photos you sent that if I do sheer (lightweight) panels I can have a thinner rod, which will help minimize the look, which I like.

Do you think sheers would look okay with the entire window, and would you prefer inside or outside mount?

Also, would you have them go all the way down to the floor if they start at the top of the window?

thanks again

What about an inside tension rod? I used those in my previous old house. Then you can choose whatever fabric keeps the sun out the best, and still open them if you want to.

thanks, @RedRyder! I think you are right

I have a house of a similar age. Half my windows are about 1” deep, some are three. I used 2” Venetian blinds in all of them and they look the same. The brackets work the same either way, I did have to adjust the valance returns so they would fit.

Cafe style rods work great.

Oh, thank you, @Home Interiors with Ease! I'll check it out!

Am wondering if plantation shutter would work? They would stick out from the window as would other types of window treatments but it might look as thought the shutters were just extensions of the window trim.

thanks @steveetheridge -- I love the idea of shutters. Most of the year these windows don't need to be covered. It's just in winter when the sunrise in the east comes in my dining window at a blinding angle! (the wonder of living in the mountains). I had one person come to the house who said that shutters would have to cover all of the trim, including the rosettes, etc, and he didn't recommend that look. I can reconsider in the future.

Tension rods with cafe curtains can be installed in a flash when you need them and removed when you don't. Many years ago some houses had two sets of curtains: heavy for winter, light for summer.

I agree with HIWE - this is a good look. Curtains can be any height, and easily be changed for different seasons.

Agree with Red Ryder on the tension rod - we have sheers in several windows with tension rods

I wonder where I can find those tiny curtain rings, I haven't seen them anywhere yet.

Restoration Hardware has cafe curtain rings and rods

Rejuvenation, Etsy & Wayfair have them if you do a search. Just make sure to double check the sizes.

Thanks to everyone for the suggestion of sheers! Here is the finished project. The sheers go down to the floor. I decided on an inside mount for a minimalist look. Less expensive than blinds or shades, but more importantly, I like this better. I hung them from the top iinstead of only on the bottom half because the blinding sun comes in the top part of the east-facing window in the morning in winter.