This paper presents a comprehensive and general optimization-based home energy management controller, incorporating several classes of domestic appliances including deferrable, curtailable, thermal, and critical ones. The operations of the appliances are controlled in response to dynamic price signals to reduce the consumer’s electricity bill whilst minimizing the daily volume of curtailed energy, and therefore considering the user’s comfort level. To avoid shifting a large portion of consumer demand toward the least price intervals, which could create network issues due to loss of diversity, higher prices are applied when the consumer’s demand goes beyond a prescribed power threshold. The arising mixed integer nonlinear optimization problem is solved in an iterative manner rolling throughout the day to follow the changes in the anticipated price signals and the variations in the controller inputs while information is updated. The results from different realistic case studies show the effectiveness of the proposed controller in minimizing the household’s daily electricity bill while preserving comfort level, as well as preventing creation of new least-price peaks.