Let I be an ideal of a ring R and let M be a left R-module. A submodule L of M is said to be -small in M provided M 6= L + X for any proper submodule X of M with M=X singular. An R-module M is called I--supplemented if for every submodule N of M, there exists a direct summand K of M such that M = N + K, N \ K IK and N \ K is -small in K. In this paper, we investigate some properties of I--supplemented modules. We also compare I--supplemented modules with -supplemented modules. The structure of I--supplemented modules and --supplemented modules over a Dedekind domain is completely determined.
