I had a drainage system installed in my lawn, which required burying some pipes in trenches cut into the lawn. After several weeks, the dirt used to fill those trenches has compacted, leaving a big dip in the lawn (in places, 3 to 4 inches deep), running the length of where the trenches were.
What's the best way to fill those depressed areas with minimal damage to the grass growing there? Should I slowly add dirt to the top of the grass, letting it fill in over time? Or should I dig up the grass (possibly damaging its roots) and add dirt underneath it?