My River Birch

We planted this river birch in our front garden area about 3 years ago. Since that time, it has more than doubled in height and width.  It has grown at an amazing speed--way faster than others in our neighborhood that were about the same size at planting.  We weren't prepared to experience growing pains this quickly. :)

Because it was taking over our sidewalk and attacking people walking up to the house, we decided it was time to trim the lower branches.  So a few weeks ago, Eric and I got to work on a beautiful fall day and trimmed off all the lower branches. I love seeing more of the beautiful bark, however, now I feel like it needs some thinning on top as well. 

I like the classic look of the river birch with the wispy light filtering branches and I feel like it has just gotten too bushy on top. I have heard of an option to thin the branches if a river birch gets too thick. It would be quite an undertaking because of the height of the tree. I am just trying to decide if this is what my tree needs. I don't want to do anything to hurt the tree since it is a beautiful tree and I love it. What do you think?