Silica aerogels with improved properties are disclosed together with methods for synthesizing such aerogels. The improved properties include lower thermal conductivity (better insulating capacity), lower acoustic velocity, lower dielectric constant and improved ductility. Greater tunability of the refractive index can also be achieved. The silica aerogels are prepared by a sol-gel processing method that provides better control of the formation or aerogel structures. Generally speaking, the improvements arise from control of the synthesis to create a morphology of primary clusters and diverse-sized secondary clusters of dense silica aerogels separated by less densely packed regions. By providing a broader range of secondary clusters and/or pore sizes and loose connectivity between clusters, reductions can be achieved in thermal conductivity and flexural modulus.