We present the notions of softc-continuity and soft nearlyc-continuity, which are weaker versions of soft continuity and soft almost continuity, respectively. We obtain several characterizations for these two concepts. We show that softc-continuity and soft almostc-continuity are preserved under soft restrictions. In addition, we investigate the conditions under which the composition of two softc-continuous and soft almostc-continuous functions is softc-continuous and soft almostc-continuous. Moreover, via softN-open sets, we give a characterization of the soft compactness of soft topological spaces over finite sets of parameters. In addition, we show that for a given soft topological space(L,Ω,F), the collection of soft regular open sets with soft compact complements forms a soft base for some coarser soft topology. We demonstrate that(L,Ω⁎,F)are all soft compacts. Furthermore, we demonstrate thatΩ=Ω⁎if(L,Ω,F)or(L,Ω⁎,F)is soft compact and soft Hausdorff. Finally, we investigate the correspondences between the novel notions in soft topology and their general topological analogs.