[old_tv_nut]

The best thing is to know the theory of AFC loops, measure what's in yours in terms of the open loop detector gain and oscillator control gain, and calculate the changes required to get quicker response and still have good damping.

Without knowing the theory, experimental determination is possible, but you have to be good at discerning what the changes you make are doing so that you can converge on a solution rather than making things worse.

The result will mostly involve reducing the size some of the filter capacitors between the phase detector and the oscillator, and perhaps changing some resistor values there also.

If you measure and calculate correctly, you will get the desired result without fail, but I have seen engineers struggle with it, generally due to botching the open loop measurements.