The normal Quine - a program that prints its own code - is a special case of an n-Quine.
An n-Quine is a program that prints code for a different program that after n iterations of printing and running will yield its own source (it has a period of n, and it does not repeat during the first n-1 iterations).
A "super Quine" is a (n>1)-Quine that is shorter than all the shortest n-Quines with smaller n (including the shortest 1-Quine = normal Quine).
When are super Quines possible? It's easy enough to think of a language where they are. But it is hard to think of an example in any general purpose language.
What factor determines the presence or absence of super Quines in a language?