By applying engineering theory, we found that in order to achieve a certain degree of stem mechanical stability, trees with low wood dry-mass density (rho(D)) need to produce thicker stems but invest less mass per unit stem length than those with high rho(D). Mechanical stability was expressed as the ability of the vertical stem to either support a plant's weight (i.e., the buckling safety factor) or resist wind forces without rupture. This contradicts the general notion that trees with low rho(D) are more prone to mechanical failure. Contrary to our results for stems, we predicted that high rho(D) can be more efficient than low rho(D) in terms of the mass needed to produce a branch of given length and resistance to rupture under its own weight. Such branches were also predicted to be more flexible. These predictions were generally in accordance with literature data for tropical tree species. This shows that differences in scaling rules associated with vertical self-loading, resistance to external forces, and the production of stable horizontal branches have important implications for the way in which different crown traits determine the balance between economy of crown design and mechanical stability.