  We investigate the noise properties of a GaAs-AlAs-GaAs tunneling structure
with embedded self-assembled InAs quantum dots in the single-electron tunneling
regime. We analyze the dependence of the relative noise amplitude of the shot
noise on bias voltage. We observe a non-monotonic behaviour of the Fano-factor
$\alpha$ with an average value of $\alpha \approx 0.8$ consistent with the
asymmetry of the tunneling barriers. Reproducible fluctuations observed in
$\alpha$ can be attributed to the successive participation of more and more
InAs quantum dots in the tunneling current.
