  We have fabricated and examined several Al single electron transistors whose
small islands were positioned on top of a counter electrode and hence did not
come into contact with a dielectric substrate. The equivalent charge noise
figure of all transistors turned out to be surprisingly low, (2.5 - 7)*10E-5
e/sqrt(Hz) at f = 10 Hz. Although the lowest detected noise originates mostly
from fluctuations of background charge, the noise contribution of the tunnel
junction conductances was, on occasion, found to be dominant.
