The attainment of self-preserving distributions by coagulation of agglomerate or aggregate particles has been investigated in the continuum and free-molecular regimes. Self-preserving distributions have been computed for agglomerates of various fractal dimensions. In the free-molecular regime, the self-preserving size distributions broaden as the fractal dimension decreases. In contrast, in the continuum regime, the distributions narrow with decreasing fractal dimension. The aggregate growth rate increases with decreasing fractal dimension of the colliding particles. This effect is more pronounced in the free-molecular than in the continuum regime. In the free-molecular regime, particles of low fractal dimension have larger cross-sectional area than particles of equal mass but with higher fractal dimension. The larger cross-sectional area per unit particle mass results in a direct increase in the coagulation rate. In the continuum regime, the effect of enhanced collision area is reduced by the increased drag of the agglomerates.