There are multiple fascinating problems and approaches connected to really small samples. It is possible to estimate confidence intervals using a single point, or there are well known problems such as German tank problem (or similar here) etc. I recently asked about forecasting with short time series. The problem is also that most of the statistical methods are designed for large samples and many theorems are described in context of "$n \rightarrow \infty$" what makes it troublesome to generalize them to really small samples. Because in general it is hard to find literature dealing with the topic of tiny samples I wanted to ask if you could suggest any?
If you're interested in how to deal with small samples in sampling (and in particular, for survey sampling), I'd suggest you read Rao, Small Area Estimation (2003, Wiley).
I also recently heard M. Hidiroglou give a general lecture about the topic (long abstract here). I'm definitely not a small sample/small area specialist, and I thought his talk was a good introduction to the subject.