Headset rattle

maybe not enough spacers between top cup and stem, or stem and top cap? if the top of the steer tube is coming in contact with the top cap, then no matter how much you squash/tighten it, you'll just pull the starnut out, and you'll still have play in the headset. put a 5mm spacer in there and try again?

+1 very good advice.

Photos would help diagnosis.

Putting pressure (small, medium or even large sized dad) on the stem will not help in any way.