The conventional understanding is that the injunction period in existing protocols encompasses at most two phases: a breach followed by a justice phase. However, the implementation of eltoo appears to necessitate a similar two-phase process comprising a breach and then a fast-forward action.

Interestingly, the use of CTV (CHECKTEMPLATEVERIFY), or emulation thereof, has proven beneficial within this context. By eliminating the requirement for round-trip communication in payment protocols, CTV facilitates "fast forwards." This simplification could potentially accelerate payment processes if it becomes widely accepted. The effectiveness of CTV can be attributed to its ability to streamline state machines directly into Bitcoin transactions through state-graph cut-throughs.

There remains a curiosity about whether alternative covenant schemes can offer the same advantages as CTV. While there is an inclination to believe they might possess this capability, confirmation of this property in other covenant mechanisms requires further examination.