It's a No!
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I recently came across a blog posted on Seths Blog where he takes the point of view that you should never turn down special requests. That you need to treat all customers differently because they are not all the same. While i agree with his point of view on yes, customers are different and do have different needs. I do not agree with treating them differently.

If someone comes in with a special request during your most busy time of year and you do not accommodate them by putting their request before others who were already in line, my opinion on that is they should not have waited until the last minute for one, and for two they should expect to hear the word “no” to their request knowing it’s your busy time.

Yes, if you turn them down they may go somewhere else, but think about if you put them first and make the other 5 customers who technically came before them wait even longer because you accommodated one, they may also go somewhere else. So which would you prefer, loosing one customer or loosing 5 customers? If it were me i’d be able to swallow loosing one customer rather than five of them.

There are two really good reasons to turn down special requests:

1. because you’re marketing yourself as extremely busy and perfectly willing to turn down good work.

2. because you want to market yourself as someone who is a rigid artist, a stick in the mud or a crotchety perfectionist. This works great for pizza places.