Reaching project goals within heavily strict deadlines. Is it possible?

We all are familiar with situations when a maximally vague project appears from nowhere and has strict time boundaries. How can we act here? We can unconditionally insist on moving further deadlines, mercilessly cutting requirements, or starting work only after doubling the team. But what if we have some opportunity to accomplish customer goals within current deadlines and without changing resource capacity? In the talk, we will consider the process that would allow us to get as close as possible to the desired result and separate the urgent from the important.