I have found that the lower the magnification the longer of a yardage span seems to be in focus. Also many cheaper non AO scopes can be adjusted very easily to change the distance in focus. I believe that if the scope was set to 9x and adjusted to be in focus at 30 yds you would have a decent view at 3x and 10 yds. The scope that came with my Crosman NVD sound like the scope you mention and does the above quite well. I'll bet that's as clear as Ohio river water in March.
I'm currently using the 32mm version of that scope and once the eyepiece vision correction was set, i haven't noticed any differences between ranges of 10 to 50 yards and power factors from 3X to 7X (at 7X i had no trouble seeing .22 pellet holes on white paper at 50 yards,) and my eye prescription is between 5 and 6 diopters vision correction--the end of the eye piece rotates to set the scope's internal focus to what you find comfortable, get it right and you won't have any eye strain after hours of shooting.. my last time out, i shot for more than 4 hours with no trouble