The ability to precisely control the thermal conductivity (kappa) of a material is fundamental in the development of on-chip heat management or energy conversion applications. Nanostructuring permits a marked reduction of kappa of single-crystalline materials, as recently demonstrated for silicon nanowires. However, silicon-based nanostructured materials with extremely low kappa are not limited to nanowires. By engineering a set of individual phonon-scattering nanodot barriers we have accurately tailored the thermal conductivity of a single-crystalline SiGe material in spatially defined regions as short as similar to 15 nm. Single-barrier thermal resistances between 2 and 4 x 10(-9) m(2) KW(-1) were attained, resulting in a room-temperature kappa down to about 0.9Wm(-1)K(-1), in multilayered structures with as little as five barriers. Such low thermal conductivity is compatible with a totally diffuse mismatch model for the barriers, and it is well below the amorphous limit. The results are in agreement with atomistic Green's function simulations.