Carbonization of pitch-infiltrated fibrous preforms during the manufacture of carbon-carbon composites poses many difficulties. Among the difficulties are the phenomena that when the fibrous pitch-infiltrated preform is held in a constraint fixture during a carbonization process, (1) the pitch may bond the preform to the fixture, (2) unequal coefficients of thermal expansion between the preform and an adjacent wall of the constraint fixture may break or stress the preform, and (3) the pitch may foam during carbonization, causing backpressure from the constraint fixture which may break or stress the preform. US 2005/0093188 A1 discloses a method for making a carbon-carbon composite preform using e.g. a steel constraint fixture. The method disclosed therein is operative, but in some cases foaming of pitch causes untidiness in the carbonization furnace. Also, it is sometimes difficult to remove the preform from the constraint fixture due to unwanted bonding.