light handlebars with area for clip on aerobars

[Emcc]

Hi there

After 5 years of lurking i finally have a question i couldnt solve myself:
I tend to ride a traditional stem and handlebar combination and sometimes like to use classical clip on aerobars (that clamp to the bar). Syntace C3 is my go-to.

Is there any light carbon handlebar out there (36-38cm) that has enough space to clamp or that is traditional round all the way?

thanks in advance