I like the frozen treat stick idea.  I keep a roll of cheap scotch tape by the saw and  when I run into a small piece that would just love to ruin my day by breaking, I just keep stick small pieces of the tape around the cut until I have moved on to more solid ground.

Make sure your blade is in with the teeth pointing down, use a blade with more t.p.i. For very fine, intricate cuts I use a blade with 28 t.p.i.

 

Mick,   Delta P-20