It has been discovered that certain nitrogen-containing thiols other than mercaptobenzothiazole (MBT) perform equivalently as accelerators in preparing asphalt polymer compositions. Typically, the crosslinker in these compositions is sulfur. Nitrogen-containing thiols containing at least one functional group —N═(SH)— have been found to be useful alternate accelerators along with activators such as zinc oxides. Particular nitrogen-containing thiols include, but are not necessarily limited to, 2-mercaptobenzoxazole (MBO), 2-mercapto-5-methyl-1,3,4-thiadiazole (MMTD), and combinations thereof.