You can move the existing header up to butt against the top plate and that will gain you a couple inches. Going with a smaller 2x header should not be done without getting the header sized with a professional.
I would check out replacing the existing header with an engineered beam. You would need to find out what size engineered beam will replace the header you now have. That may save you several inches in height.

THIS IS US YELLING AT YOU.....just kidding.

Talk to an engineer. The only way is to either go down and take out some stucco or go up and do as Strong said to move that header.

You can perhaps gain some more space by putting in an engineered or flitch beam in that current headers location.

Either scenario will require interior demolition to expose the wall internals so be prepared for that eventuality if that is the case.

and lvl could also be tripled up for even more strength if you have the room .
a steel beam will give you the most clearance if needed.

you could even remove the bottom top plate if no jack studs are used.

Thank you all so much for your helpful responses. I checked with a structural engineer. He charges $750 for his services so that's out. I researched lvl, flitch beam and steel beams. My husband has a wire welder so he could put in a steel beam if necessary.

A friend visited yesterday who used to be in the remodeling business. He's a perfectionist and does very nice work. He said that the standard requirement for a four foot opening is a 4 x 4. He thought that the builders must have put in the large header over our window because they happened to have a piece left over. He seemed pretty confident of his information but since you guys are the window experts, I'm a little hesitant to believe that a 4 x 4 would meet code. From what you guys said, I'm thinking that sandwiching a 1/2" steel plate between two pieces of wood would be a safer bet or maybe a 4 x 5" steel beam made of 1/4" steel?

+1

Buy the steel and make it a flitch beam. You will not have any issues after that.

Thank you for your input, Windowswashington. It is much appreciated. We'll go with that plan.

Got charged 5,000.00 to replace rotted header front rm room window measuring 120 inches across!! Contractor had to lift house 2 inches s beam was sitting on window frame. 1reframed window and new drywall whole front wall, fixed sagging wave if sofft from one of house to thee other. I think Ivpaid to mych!! Any comments. Appreciated. Ty j.

Impossible to tell from just a small description. Would really needed t have seen it all before any work took place and had a chance to evaluate.