In this paper, we work out modules with the property that every z-closed submodules are essentially embedded in direct summands. This class of modules properly contains the class of CS-modules as well as some of their generalizations. It is shown that the class of modules with former property is closed under direct sums under a certain condition. Taking into account this case, we obtain several results on the inheritance of the latter closure property. Moreover, we consider the behavior of this new property for extensions of modules.