It's worth considering when relays do not work very well. I'll assume a relay structure where responses are game force and shape otherwise resolves before strength, controls, or honor location.
The bad situations seem to be:
(1) Relayer has shortage somewhere, and the best contract is very dependent on describer's honor holding opposite that shortage.
(2) 3NT is a likely contract, but there is a suit where we hold five or fewer cards combined and where relayer has no top honors (i.e. possible stopperless suit).
(3) Relayer has a lot of shape and/or a self-sufficient suit and cares a lot more about particular control cards than about shape or total values/controls.
(4) Declarership of a particular contract is extremely important, and continuing to relay normally can potentially cause describer to name this denomination (thus wrong-siding the contract).
There are various ways to accomplish these goals, but it's worth noting that relayer often has multiple opportunities to break the relay. Breaking relay by a huge number of steps is very inefficient and to be avoided. Some ideas:
Relay breaks for reason (2) usually are late in the sequence, after describer has resolved most of his shape. This is because relayer generally won't know about the "danger suit" until this point (i.e. if it could still be 3 opposite 3 there is not much need for honor cards). It makes sense to assign relay breaks that "barely fit" below 3NT to this purpose when possible.
There are several ways to deal with relay breaks of type (1), depending on what you want to happen after the break. One possibility is that the relayer/describer roles flip (reverse relay) but this will only enable to resolve a small number of distributions (i.e. just three suiters in tosr) and there will be some hands you just have to stick out with the regular relay. Another possibility is to "revert to natural bidding" -- the main issue here is that this is not very efficient and it may be better to "swap" some meanings around (i.e. a NT bid should never be a balanced hand here since that would just relay). A last possibility is to have describer continue to describe (losing a step or two) but with the orders not to count honor cards (other than ace) in relayer's short suit, and to treat any 3NT signoff as conditional on honors opposite the short suit. One approach I like is to have opener's cheapest non-relay call announce shortage in the suit describer has just shown, allowing to lose only one step as often as possible (i.e. 1♣-1♥ showing spades and 1♠ by opener shows 2+ spades and relays whereas 1NT shows 0-1 spade and continues relay up a step; 1♣-1♥-1♠-1NT showing spades with hearts and then 2♣ by opener is 2+♥ also and 2♦ is 0-1♥).
Type (3) relay breaks are usually good meanings for skipping multiple steps at a time, as we pretty much have to give up shape relay at this point.
Type (4) is tricky; most often the contract that needs to be "sided" is 3NT and relay breaks to bid notrump (especially if not the cheapest break) can fairly often be given this meaning. Another one that comes up if using 4♦ as "end signal" is trying to right-side hearts -- with one partner I play that jumps to 4♥ when hearts have not yet been named are basically "to play" whereas all other signoffs above 3NT go through the 4♦ "end signal" (so a jump to 4♠ for example would not be "to play").

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