The structure of colloidal clusters formed by long-range attractive interactions under diluted conditions is studied by means of Monte Carlo simulations. For a not-too-long attraction range, clusters show self-similar internal structure with lower density than that typical for diffusive aggregation. For long-range interactions, low kappa, nonfractal clusters are formed (dense at short scales but open at long ones). The dependence on the volume fraction shows that more-compact clusters are grown the higher the colloidal density for diffusive aggregation and attraction-driven aggregation in the fractal regime. The whole trend is explained in terms of the interpenetration among aggregates. In attraction-driven aggregations, the interpenetration of clusters competes with aggregation in the tips of the clusters, causing low-density clusters.