What birds or small game species are you trying to kill?
Anything inside of 25 yards is wtat I consider "close" and even a 20 gauge will chew them up bad, esp with a MOD choke. Try backing off to 25 yards, then 30 yards, then 35 and 40 and 45 yards.
Using butcher paper (if you can get it cheap) or the ends of rolls of newsprint paper, make a frame from 2X4's large enough to staple a 3 or 3 1/2 foot square papper sheet. Draw a 30" and 36" circle on that paper sheet with a 2 or 3 inch dot in the center. Use that dot as your pattern center at the ranges you try your various loads and shooting conditions.
When I've shot a 20 gauge my shots 95-plus percent of the time are within 25 to 45 yards. 25 yards was "close" and 45 yards "far away." Average is 30-40 yards. I usually use #8's, #7 1/2's or #6's. Anything bigger than #5's are starting to give you a really sparse pattern and in that light weight singleshotgun, anything over a hi-vel 1-ounce load will thump your shoulder good!
But what game are you shooting? And at what ranges?