I never used to be a "process" person.
In fact, it goes against the very grain of my creativity sometimes. But as I've grown as a designer and more importantly as a creative business professional, I've learned along the way that there is much to be gained from setting a proper order to the proverbial chaos that is "working with clients."
As it is tied to project management, a process certainly makes sense. But it's amazing how quickly things can become messy when your client suddenly makes a seemingly-unreasonable demand. How to find the balance between satisfying the client need while making sure to dot all i's and cross all t's is an art form in and of itself, and it requires a certain amount of working smart (vs. the alternative, working hard.)
Let's say you and your client have agreed on a deliverable date, but, suddenly the date moves up due to a surprise new business meeting that the client has secured with a prospect. They still need what they've hired you to deliver, but they need it sooner. You, of course, feel added pressure to make them happy and deliver something great, but with the limited time, you're not sure you can pull it off. You don't want to skip certain steps in your process because you know that the time spent doing them adds value to the final piece.
What to do?
This is where your client relationship experience and business sense comes into play. Each situation is different, so take a step back and look at the larger picture. Ask yourself - will going above and beyond (late nights, long hours) pay off in other ways? Will it build a level of trust with my client so that they'll keep coming back? If the answer is yes, then you do what it takes to get the job done - whether that means abbreviating parts of your process or prioritizing this client over others in order to keep them happy.
If you absolutely cannot stray out of order in your process, there are some options. You can explain to the client that the original deliverable may not be feasible in it's entirety by the earlier date - but you are able to offer a solution that is. For example, client wants a new website in 4 weeks instead of 8, but you realize that's not possible. So you offer to make a microsite or landing page live within that timeframe so that they still have a digital presence, and then flesh it out after the earlier date has passed. Explain that the sooner delivery date may incur some rush fees (or put this in your SOW ahead of time...) but you'll be happy to comply. Most clients are reasonable when you try to help them don't just recede when the going gets tough. Having been client-side myself, I know they'll appreciate the effort and take that into account when doling out new work.
Really, there's no absolute answer.
The only advice is to evaluate each situation with a sense of flexibility and perspective, and realize that by using some great communication skills along with viewing each situation at face-value, you'll have a lot more success. The reason you're in this business, remember, is to help clients achieve their goals.