Crowd Sourcing
From 4docs
Crowd sourcing is all about leveraging networks and the web to raise financing towards your film project. You put your film idea out in the world tagged with it's key themes and info about you and ask interested parties to put up funding towards the project.
With crowdsourcing you're not normally giving away any rights to your film and you're actively building a future audience for the project and potentially a support network for future films.
Even where you don't need to raise the full finances you can supplement your completion budget through crowdsourcing without it affecting your ability to sell the film on.
Filmmakers have found new and innovative ways to do this, sometimes offering different levels of project ownership (credits / screenings / dvds) for money through their own websites. There are also specific sites dedicated to crowdsourcing for film - and that most definately includes short documentary film!
Sites to check out:
Case studies
Zed Nelson's short film Shelter in Place raised an additional $7,500 through donations via IndieGoGo