Should I hold my CVT gearbox on the brake?

Having replaced the earlier model we now have a Jazz CVT which does twice the mpg on narrow hilly Cornish lanes. I drive as economically as I can but wonder what happens when I hold the car on the brake...

Should I put my automatic car in neutral when stationary?

I have Mercedes E220 Blue Tec. I would like to know that whenever I am idling in stationary mode, should I dis-engage the gear to neutral, or should I simply keep my foot on the brake with the car in drive...