Optimizing CDT for subdividing triangles

[proc-sim]

I'm running CDT on triangles in order to subdivide them into smaller triangles. Since the domain of each CDT operation is already triangular, do I still need to create/remove the supertriangle? I'm wondering if there's any optimization potential here (skip supertriangle addition/removal routines when domain of all constraints/points is already triangular)...but I don't know enough about the internal workings of CDT to understand whether adding a supertriangle is a necessary precondition for computing a CDT in all cases...thanks!