Keep morels fresh during and after picking by keeping them dry. Line a 5-gallon bucket with one of the brown paper bags and take it along while foraging. Place newly picked mushrooms inside of the brown paper bag, as it will provide protection from bruising and wick away moisture.
Pick as many morels as you can find. Avoid picking morels that look discolored, have wilted sides, have bites taken out of them or are mushy or slimy. When the paper grocery bag inside of the bucket is half full, replace it with a new one. Fold over the top of the bag to keep the morels dry and secure.
Spread newspaper sheets out on kitchen counter. Carefully place the morel mushrooms on the newspaper. Look at each morel closely for bugs, dirt, sand, leaf matter or pine needles. Blow away particles of sand or bug larvae lodged in the many nooks and crannies of the mushroom cap with a gentle shot of compressed air.
Transfer the cleaned mushrooms to a new brown paper bag and place it directly in the refrigerator. Use mushrooms within four days for the best level of freshness.