NAR released two "flat fold" trauma dressing bandages, in 6 inch and 4 inch. If you do not have a trauma bandage in your bag, for EDC or otherwise, you should probably grab one of these. I carry a 4 inch in my EDC bag.
If you are going to buy the above items please refer to this post talking about essential medical gear everyone should have (and know how to use). I will be posting up a bigger, more detailed med kit post later one once I get the concepts flushed out.