other breast leaking

D • Wife. Mama. Full-time career. 1 sweet boy and boy/girl twins

Ok ladies, I'm a FTM and still trying to figure out this breastfeeding thing. how do you keep the other breast (not being fed from) from leaking so much when you're feeding? I usually shove a burp cloth in there to absorb when the milk let's out but it's hard and still messy. Here is a picture of when I thought I had a cloth in there but it had apparently moved during the feeding. Poor little guy was soaked. Recommendations?