The present invention relates to acid-soluble cement compositions that comprise cement kiln dust (“CKD”) and/or a natural pozzolan and associated methods of use. An embodiment includes a method of cementing comprising: placing an acid-soluble cement composition in a subterranean formation, wherein the acid-soluble cement composition comprises a hydraulic cement, a component selected from the group consisting of CKD, pumicite, and a combination thereof, and water; allowing the acid-soluble cement composition to set; and contacting the set acid-soluble cement composition with an acid to dissolve the set acid-soluble cement composition.