Suppose you have a Dehn presentation $\langle X \mid R \rangle$ of (say not the free group) a hyperbolic group.
Has there been some work done on changing this presentation, e.g. adding a relation ("well chosen one") or else some Tietze transformations such that the obtained presentation is still a Dehn presentation?
Edit: It should be emphasised that I do not want to change the group in question. Hence I am looking for a way to change the presentation for this particular group but not the property of being a Dehn presentation.
Since a priori there should be many different ways to write down a Dehn presentation for the same group but how to switch between these? Maybe finding some "optimal" one (where optimal is of course quite vague at this stage).