A carbon molecular sieve (CMS) membrane is made by pyrolyzing, to a peak pyrolysis temperature TP, a hollow fiber membrane having a polymeric sheath surrounding a polymeric core, anti-substructure collapse particles present in pores formed in the polymeric core help prevent collapse of pores formed in the hollow fiber membrane before pyrolysis. The anti-substructure collapse particles are made of a material or materials that either: i) have a glass transition temperature TG higher than TP, ii) have a melting point higher than TP, or ii) are completely thermally decomposed during said pyrolysis step at a temperature less than TP. The anti-substructure collapse particles are not soluble in a solvent used for dissolution of the polymeric material of the core.