Random three- and four-amino acid copolymers having lengths of 14-, 35- and 50-amino acid residues are provided. The random copolymers have amino acids alanine, lysine and one or more of the hydrophobic amino acids valine, phenylalanine, tryptophan and tyrosine. Random three-amino acid copolymer FAK efficiently suppressed EAE induced in SJL/J (H-2S) mice with the encephalitogenic epitope PLP 139-151. Random four-amino acid copolymers VYAK and tryptophan-containing VWAK were efficacious in alleviating severity and duration of symptoms of EAE induced by MBP 85-99 (SEQ ID NO:2), in a humanized mouse model expressing genes for both an HLA-DR-2 linked to multiple sclerosis (MS) in humans and for a T cell receptor from an MS patient.