Methods of cementing subterranean zones using cement compositions containing biogradable dispersants are provided. The methods are basically comprised of the steps of preparing a hydraulic cement, a biodegradable dispersant comprised of polyaspartic acid containing side chains formed by reacting one or more side chain chemicals with said polyaspartic acid and sufficient water to form a pumpable slurry, placing the cement composition into a zone to be cemented and allowing the cement composition to set into an impermeable solid mass therein.