Is more or less impulse better during a collision (safety-wise)?

My assignment for my biomechanics class is to do a presentation on impulse to the class. I'm trying to explain it with an example of how football helmets protect your head by increasing the amount of time it takes for momentum to come to zero. I know that by increasing the amount of time, you decrease the force of the impact.

To ensure safety, do you want more or less impulse during a collision? I read on some website that impulse stays constant, but only force and time change. This doesn't make sense to me. Why does impulse stay constant?