Space-filling designs are a convenient and effective approach for exploring the input space for experiments. However, standard choices for these designs strive to provide uniform density of points throughout the region of interest. There are numerous situations where flexibility to adapt the density of points to match specific design objectives would be advantageous to maximize the efficiency of the design. In this paper, we propose non-uniform space-filling (NUSF) designs to achieve a

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... ified desired density distribution of design points across the input space and demonstrate how to implement NUSF designs in different ways to provide the experimenters with flexibility to match their goals. The approach is flexible for a variety of scenarios where the experimenter wishes to control the density of points throughout the region while still preserving the space-filling characteristic. Details are provided about how to translate a problem into an appropriate weight structure to generate several designs which can then be compared using graphical methods, including the Closest Distance by Weight plot, to determine if the desired characteristics have been achieved. The methods are demonstrated with two real examples with different requirements for design point placement.