Smallest I have seen lately are the 4 1/2" Nils.
Cabelas actually has the high velocity model on sale for $104 right now.
http://www.cabelas.com/product/Nils-USA-High-Velocity-Hand-Auger/1089564.uts
If you have good clear ice it is easier to put the transducer (as long as it's a flat ice ducer) on the ice (shovel away snow) and with the sonar on pour a little water on the ducer to couple it to the ice and you can read depth easily. I have read depth through more than 5' of ice and I have even marked fish through the ice.