In this study, by using somewhere dense sets and cs-dense sets, we introduce and investigate the notions of almost $SD$-compact and almost $SD$-Lindelöf spaces, nearly $SD$-compact and nearly $SD$-Lindelöf spaces, and mildly $SD$-compact and mildly $SD$-Lindelöf spaces. We show the relationships between them with the help of illustrative examples. In addition, we characterize them and study their behaviours under some types of mappings.