  We study the scaling of the average cluster size and percolation strength of
geometrical clusters for the two-dimensional Ising model. By means of Monte
Carlo simulations and a finite-size scaling analysis we discuss the appearance
of corrections to scaling for different definitions of cluster sets. We find
that including all percolating clusters, or excluding only clusters that
percolate in one but not the other direction, leads to smaller corrections to
scaling for the average cluster size as compared to the other definitions
considered. The percolation strength is less sensitive to the definitions used.
