A stress-decoupling device and methods of using same in a cooled grazing-incidence collector (GIC) mirror system are disclosed. A method includes providing a cooled GIC shell, providing input and output primary cooling-fluid manifolds, and fluidly connecting the cooled GIC shell to the input and output primary cooling-fluid manifolds through respective stress-decoupling devices. An exemplary stress-decoupling device includes inner and outer bellows that define a sealed cavity filled with a gas. An expansion-limiting member within the sealed cavity limits the expansion of the inner bellows due to the pressure of the cooling fluid flowing therethrough. The stress-decoupling device reduces or prevents the communication of stress from parts of the GIC mirror system to the GIC shells. Stress-decoupling systems and methods for a cooled spider as used in a GIC mirror system are also disclosed.