Fuel injectors with intensified fuel storage and methods of operating an engine therewith. At least one storage cavity is provided in the intensifier type fuel injector, with a check valve between the intensifier and the needle chamber and storage cavity preventing loss of injection pressure while the intensifier plunger cylinder is refilling with fuel. This provides very efficient injector operation, particularly at low engine loads, by eliminating the wasted energy of compressing, venting and recompressing fuel for injection. Various injector designs and methods of operating the same in an engine are disclosed.