The wonderful gift of being an independent filmmaker is that you don't have producers and studio execs asking questions like, "but what if she had a ditzy best friend? Ditzy best friends are hilarious. You know what's also testing really well right now? Chimpanzees. Can we have a scene with a chimpanzee in it?" These producers and execs mean well, but their interest is attracting more people to see the movie (and thus make more money), not tell a better story.
Being an independent filmmaker means you are in charge of the story. Nothing has to be put on the screen that you don't want there.
There are a lot of corners that have to be cut when you don't have studio backing. Not having the budget of Spider-Man 3 means you're probably not going to have a lot of CG action sequences. You're going to have to be thrifty with your time and money. You might not be able to afford sets, lighting, or film. And so you plan your shoot accordingly.
But you know the one thing that's not affected by the budget? The script. The script is free. The CG antics might need to be reduced and the number of locations might need to be reconsidered, but the story, as it's written, doesn't cost a dime. The dialog can be polished ad nauseum. As the screenwriter, you may have a deadline, and you may be working with people who have a very specific film in mind, but you really have no excuse for churning out a lackluster script.
The script should shine above all other things. The lighting and the acting and the locations should fail the script. The script shouldn't fail the actors. Walking into an independent film, the audience expects not-the-best acting and not-the-best lighting. So impress them with your script. Show the audience why this movie got made. Because if your movie has not-the-best lighting and not-the-best acting and not-the-best sound and not-the-best camera work and not-the-best script . . . then what is there to enjoy?