String Ringing

first of all nice lessons muris'

I would like to ask a question about strings ringing.

What is the most effictive way to stop the snares from ringing if you play for instance a solo and you go up a strings. And don,t have any problems when a go down the strings then I mute the strings with the palm of my hand , but when I go up the strings I notice that it is not always so easy to stop them from ringing.

thanks

John