Have you considered hanging room darkening curtains over the 2" blinds?

Yes, we have tried blackout curtains. We want white and they don't block enough light, plus they let out too much light on the sides. Thanks though

I think room darkening cellular shades work the best for blocking out light. They're still one of the best selling treatments in the 21st century. Roman shades with a black out liner are a close 2nd. If you use romans I would make them flat romans but have to be careul not to clash fabric with the drapes. here's a pic of an IM cellular. Notice light coming through at the sides. Panels will take care of that. Otherwise if they were OM less light would come through.

Here is a link that might be useful: Inside Mount Room Darkening Cellular Shades

How are "pleated" shades different than cellular? I just saw these on blinds.com, and a blackout option can be added...

thanks

Pleated are just that......pleats........as though you folded the fabric to make a fan.
Cellular, when viewed from the ends looks like cells, as seen in the pic below.

Bob is correct that light comes thru the ends of IM shades, but it will also come thru OM. Light finds it's way thru any opening!

You can use side panels with a roman blind.

But for room darkening, we go with the room darkening roller shade which can be hidden up and out of the way under a window valance....that's what we do in our bedrooms. They also help keep the rooms warmer at night.

Annie, what brand of roller shades do you have? I always think of the junky ones that won't work....haha