I have been getting quite a few customers now who come in for urgent design work. To accommodate this their job sheet is pushed ahead and we go out of our way to rush it to meet their deadlines. The customers then come back and forth for weeks with alterations to the design and the 'urgent' deadline keeps getting pushed out and changed. Do you have any advice on how to manage this, as I feel it is a bit of a sneaky tactic of the impatient customers to jump the cue.
They're doing it because it works. :) And it's not fair to your other clients. If it were me, I wouldn't let them push to the head of the line. Unless, as Zach said, you charge a substantial rush fee.
When I have a new client, we have a very long initial meeting, and work through most of the project details. This really helps smooth out the rest of the process and reduces changes.
And you should charge for the changes.
Rush charges should be part of your initial briefing and spelled out clearly in your contract.
The client should spell out the deadlines as much as possible. If the client then comes back after the contract is signed and says "but I need this a week sooner!", you should have a section in the contract which explicitly says something to the effect of "Designer will endeavor to meet all Client deadlines. If Client requests rush service, a surcharge of X% will be added to the total invoice." What X% is will depend on the client, your annoyance level, how often this client pulls this trick, and how important this client is to you financially. Then you document the crap out of the alterations and the deadline changes so you can add a ton of line-item charges to the invoice.
When the client calls and asks you for the job a week sooner, you remind the client "Per our contract, this will cost you X% more. Are you okay with that?" Keep mentioning that hurrying costs money.
Alternately, again depending on your financial situation and the importance of the client, you may choose to say "I can't rush this." You can say there are other clients who are ahead in the queue, other rush jobs ahead in the queue, or the old advice-column standback, "I'm afraid that won't be possible." (The other version of this I like is "I'd like to accommodate you, but I'm afraid I can't right now.")
As DocPixel points out, your clients are training you to allow this. Push back.