This invention relates to a method for treating an angiogenesis-related disease. The method includes administering to a subject in need thereof an effective amount of a piperazinedione compound having the formula: In the above formula, each of and , independently, is a single bond or a double bond; A is H or CH(RaRb) when is a single bond, or C(RaRb) when is a double bond; Z is CH(RcRd) when is a single bond, or C(RcRd) when is a double bond; each of R1 and R2, independently, is H, C(O)Re, C(O)ORe, C(O)NReRf, or SO2Re; and each of Ra, Rb, Rc, Rd, Re, and Rf, independently, is H, C1-C6 alkyl, aryl, heteroaryl, C3-C8 cycloalkyl, or C3-C8 heterocycloalkyl; or Ra and Rb taken together are C3-C8 cycloalkyl, C3-C8 heterocycloalkyl, aryl, or heteroaryl; or R1 and Ra or R1 and Rb taken together are C3-C8 cycloalkyl, C3-C8 heterocycloalkyl, aryl, or heteroaryl; provided that one of Rc and Rd is aryl or heteroaryl.