Box window furnishings?

Hi everyone, we are adding a box window (and eventually building a windowseat) to our house plans in the master bedroom. We've had it costed and really want to go ahead, but now I am clueless as to what kind of window treatment to use. We have had a large bay before and used a combination of blinds and swags, but were still left with a few annoying light gaps. I looked on line but a lot of the pictures are of bays, not box- so the window angles are different and/or they have left them bare for views. As it will be an east facing window we need to block out morning sun.

How to get away from the gaps other than a curtain over the window from wall to wall which will hide the box when they are drawn?

We are having a box window in our Master as well and it faces east as well so I will be watching this post also. We have box window in our current home and have romans on it. Two small on the short sides and a big one along the main window area but not fully blockout so not great for sleeping so not doing that again. I am thinking about shutters. Love the look but not sure if they will block out enough light for a bed room. Other wise you can alway get your curtains done so the pull further back that normal if you have the wall space to accomodate this. Hope this help but will be looking forward to others responses

Just bumped. All suggestions welcome!

Anyone with shutters, please let me know if they would work in this situation and how good are they to block out light?

I love the look of them