We show that randomness of the electron wave functions in a quantum dot con
tributes to the fluctuations of the positions of the conductance peaks. Thi
s contribution grows with the conductance of the junctions connecting the d
ot to the leads. It becomes comparable with the fluctuations coming from th
e randomness of the single-particle spectrum in the dot while the Coulomb-b
lockade peaks are still well-defined. In addition, the fluctuations of the
peak spacings are correlated with the fluctuations of the conductance peak
heights.