Bird Brains

At the top of our living room we have two large windows. On occassion a bird will fly right into one of the windows. If you are sitting in the living room it is sure to scare the crap out of you. It sounds like a gun shot. Lots of times we will go outside to find a bird flopping around in the grass trying to collect his marbles. Note the grease spots on the window where birds have plowed into it. The one on the left is wing span and all. The only reason I can think that they fly into it is that it reflects the pine trees from behind our fence. We have not cleaned those windows for quite some time thinking that it might help, apparently it hasn't :(
This is the 2nd dove 2 days in a row that never knew what hit him. Kind of sad. This one was so pretty.
Anyone have any suggestions to help out with this problem?