I do that, but I do clarify that I'm fully booked "for x and y nights in December". I usually get to the point where I have to do it as I get fed up with the endless last minute enquiries for dates that I'm already booked.
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The free quote one is just stupid - I'd actually refuse to contact a client if they hit me with that bull:Censored::Censored::Censored::Censored:.
As for being fully booked - depends really, I'm limiting the amount of work I'm taking on over the year in total and month by month so I am fully booked for several of those - the nights I'm working are irrelevant.
The fully booked one is a funny one as what do you class as Fully Booked, however I also think (and something I am guilty of) is the likes of "not many dates left"
People don't really care - the only thing that is important is whether you are free or not on their date. Someone with only 1 booking may be booked out on their date, whereas someone with 200 bookings may still have their date available.
The "not many dates left" one is in sales terms, trying to force a customer's decision....its all about scarcity.
If someone's thinking about hiring you and they realise that dates are going fast (no matter which nights of the week you work), they're in theory more likely to book sooner in case you become booked should they wait around to make their decision.