Dormer England
Dormer England 1-1/4 H.S. Taper Shank Drill Bit
You will find that 1/4 in is thin enough to fit but thick enough to last.
NEW Dormer England 1-1/4 H.S. Taper Shank Drill Bit
A nice touch is how Thermal Transfer Products LTD includes spare hardware in the box.