An impact-absorbing protective structure comprises one or more compressible cells. Each cell is in the form of a thin-walled plastic enclosure defining an inner, fluid-filled chamber with at least one small orifice through which fluid resistively flows. Each cell includes an initially resistive mechanism that resists collapse during an initial phase of an impact and that then yields to allow the remainder of the impact to be managed by the venting of fluid through the orifice. The initially resistive mechanism may be implemented by providing the cell with semi-vertical side walls of an appropriate thickness or by combining a resiliently collapsible ring with the cell. After the initially resistive mechanism yields to the impact, the remainder of the impact is managed by the fluid venting through the orifice. The cell properties can be readily engineered to optimize the impact-absorbing response of the cell to a wide range of impact energies.