An x-ray source comprises a structured anode that has a thin top layer made of the desired target material and a thick bottom layer made of low atomic number and low density materials with good thermal properties. In one example, the anode comprises a layer of copper with an optimal thickness deposited on a layer of beryllium or diamond substrate. This structured target design allows for the use of efficient high energy electrons for generation of characteristic x-rays per unit energy deposited in the top layer and the use of the bottom layer as a thermal sink. This anode design can be applied to substantially increase the brightness of stationary, rotating anode or other electron bombardment-based sources where brightness is defined as number of x-rays per unit area and unit solid angle emitted by a source and is a key figure of merit parameter for a source.