The transport properties of artificially engineered superlattices (SLs) can be tailored by incorporating a high density of interfaces in them. Specifically, SiGe SLs with low thermal conductivity values have great potential for thermoelectric generation and nano-cooling of Si-based devices. Here, we present a novel approach for customizing thermal transport across nanostructures by fabricating Si/Si_1-xGe_x SLs with well-defined compositional gradients across the SiGe layer from x = 0 to 0.60. We demonstrate that the spatial inhomogeneity of the structure has a remarkable effect on the heat-flow propagation, reducing the thermal conductivity to ~2.2 W·m^-1·K^-1, which is significantly less than the values achieved previously with non-optimized long-period SLs. This approach offers further possibilities for future applications in thermoelectricity.