As Olin notes, if this is for house wiring it will need to meet regulatory limits.
If safety is a concern you may be concerned with eg temperature rise.
"Smallest diameter possible" may be to fit in a duct etc - you need to say WHY for this to be able to be answered well.
Here is a table that will both help and confuse. Note that at lower current levels there are two standards that vary widely. See also the note re contacting your local electrician re legality.
All that said, if smallest diameter is really your aim, then something like 26 gauge AWG is liable to be "fairly safe".
which only gives the very conservative rating and suggests you'd want about 18 gauge (likely to be unnecessary but YMMV).
As a general guide: http://en.wikipedia.org/wiki/Standard_wire_gauge