I give plenty of breaks throughout the day so that there really is no need for them to leave the room for an 'emergency'. I tell them that if its an emergency, then they can sign out and go. I have a sheet for them to write the time they leave and the time they return. If they are gone too long (I set the time to 3 minutes - we are a couple doors down from the restroom,) then they must owe me some time to make up for it. (Loss of free time or recess time...) I tell them that if they are having to use the restroom a lot then I call their parents because they might want to take them to the doctor to make sure everything is okay. I play it up a little

but I say it very seriously so they know that I will actually call. (I haven't ever had to call a parent... ) Oh - and they get 3 minutes a DAY, so only one emergency break per day.
In the past I have given my kids 'chips' for restroom breaks - I gave 5 per week. I just used some plastic colored discs and put their initials on them - you can use an egg carton to keep them in so when you hand them back out at the beginning of the week it goes quick. When they had to leave for a break then they gave me a chip. At the end of the week, they traded their left-over chips in for whatever...
As far as the pair thing - I'm not sure if I understand it - so if a student has to use the restroom during class time, another student has to go with them for safety reasons? If so, could you have a classroom job for it? One specific student could them? Maybe let them know that you only choose resonsible students for that job... Or maybe you could strategically pair them so that that same pair goes every time? Put the more responsible students with the ones that seem to goof around?
I met this teacher that use a really great strategy for tattleing, restroom break issues, and things like that. He kept a small memo pad and pen with him everywhere he went - every time a student asked to use the restroom or wanted to tattle... he would take it out, flip to page, and begin to write everything the kid said like he was taking notes for a report. He did it very seriously... He would slow the student down in his story and write EVERYTHING, noted the time, place, etc... It usually only took one time for the kids to not do it again. Very funny to watch, especially the kids face when he whips out the memo pad and pen

. I wish I had the personality to pull it off - my kids would see right through me and play it up I'm sure.
