A process for making a multi-component hollow housing comprises injecting a first plastic material into a first mold cavity and causing it to solidify to form a first component, whereby the first plastic material shrinks lengthwise; injecting a second plastic material into a second mold cavity having the first component transferred thereto and causing the second plastic component to solidify to form a second component, the second component comprising a tolerance-elimination element that is longitudinally attached to the first component at one of the ends thereof, wherein a length of the shrunk first component is at least ten times greater than a length of the tolerance-elimination element, and wherein an absolute lengthwise shrinkage of the second plastic material forming the tolerance-elimination element is at least ten times smaller than the lengthwise shrinkage of the first plastic material; at least partially overmolding an intermediate part comprising the first and second component with a third plastic material in a third mold cavity, thereby forming the multi-component housing in which the tolerance-elimination element is at least partially overmolded by the third plastic material, and wherein the third plastic material forms at least a portion of an outer surface of the multi-component housing; and removing the multi-component housing from the core.