  We have studied one-dimensional cellular automata with updating rules
depending stochastically on the difference of the heights of neighbouring
cells. The probability for toppling depends on a parameter lambda which goes to
one with increasing slope, i.e. the dynamics can be varied continuously. We
have investigated the scaling properties of the model using finite-size scaling
analysis. A robust power-law behavior is observed for the probability density
of the size of avalanches in a certain range of lambda values. The two
exponents which determine the dependence of the probability density on time and
system size both depend continuously on lambda, i.e. the model exhibits
nonuniversal behavior. We also measured the roughness of the surface of the
sandpile and here we obtained an universal behavior, i.e. a roughness exponent
of about 1.75 for all values of lambda. For the temporal behavior of the mass a
$f^{-\phi}$ spectrum is obtained with an exponent phi close to 2 again for all
lambda-values.
