What a flat fee is actually for
The billing structure changes how the last hour of the day feels.
I charge one number per party for the session. That number covers reading the file, the pre-mediation calls, the day itself, drafting help on the agreement, and the follow-up calls if we do not close in the room.
The reason is not that flat rates are cheaper, though for a full day they usually are. The reason is that hourly billing puts a meter in the room at the worst possible moment. At four o'clock the parties are three moves apart and everyone is tired. That is exactly when a lawyer starts calculating what another hour of the neutral costs the client, and exactly when nobody should be doing that arithmetic. Cases settle in the last hour more often than in any other hour of the day.
It also removes an awkward conversation about the work that happens outside the session. Reading your position statement carefully takes time. So does the call two weeks later when a defendant's position has quietly softened and nobody wants to be the first to say so. If I billed for that time, some of it would not get done, because you would reasonably decline to authorize it.
The tradeoff is that a case which settles in ninety minutes costs the same as one that takes six hours. I have made my peace with that. Predictability is worth more to most clients than a precise accounting, and it lets me spend the day on the dispute rather than on the clock.