i have used both types of peeps and i actually like the one like you have now better. although they are just a personal preference. the rubber cord will pull the peep to the same position everytime, but it is also adds a little noise to the bow with rubber tube. plus sometimes the rubber tube breaks (happened in my case) and then you are really messed up until you take it back to the bow shop and get the tubbing replaced and the peep reset. i currently have just the circle inline peep like you described and have had absolutely no problems with it. the problem that you are having or that you possibly could have with it moving is that with the new string every time you shoot the bow the sting is stretching and that is moving the peep, my bow shop suggests that on a new bow or with a new string to shoot the bow a couple hundred times before you ever get a peep put on there. then your string will be settled and broke in. there is no prob. with putting it in now it is just that as the string stretches you may have to keep adjusting it. but it is nothing to really worry about b/c you still have plenty of time to get it settled it.