In this paper we introduce the concepts of CD-rings and CD-modules. Let R be a ring and M be an R-module. We call R a CD-ring in case every cosingular R-module is discrete, and M a CD-module if every M-cosingular R-module in σ[M] is discrete. If R is a ring such that the class of cosingular R-modules is closed under factor modules, then it is proved that R is a CD-ring if and only if every cosingular R-module is semisimple. The relations of CD-rings are investigated with V -rings, GV -rings, SC-rings, and rings with all cosingular R-modules projective. If R is a semilocal ring, then it is shown that R is right CD if and only if R is left SC with Soc(R_R) essential in RR. Also, being a V -ring and being a CD-ring coincide for local rings. Besides of these, we characterize CD-modules with finite hollow dimension
