In recent years, researchers have proposed numerous advanced load scheduling algorithms for smart homes with the goal of reducing the grid's peak power usage. In parallel, utilities have introduced variable rate pricing plans to incentivize residential consumers to shift more of their power usage to low-price, off-peak periods, also with the goal of reducing the grid's peak power usage. In this paper, we argue that variable rate pricing plans do not incentivize consumers to adopt advanced load scheduling algorithms. While beneficial to the grid, these algorithms do not significantly lower a consumer's electric bill. To address the problem, we propose flat-power pricing, which directly incentivizes consumers to flatten their own demand profile, rather than shift as much of their power usage as possible to low-cost, off-peak periods. Since most loads have only limited scheduling freedom, load scheduling algorithms often cannot shift much, if any, power usage to low-cost, off-peak periods, which are often many hours in the future. In contrast, flat-power pricing encourages consumers to shift power usage even over short time intervals to flatten demand. We evaluate the benefits of advanced load scheduling algorithms using flat-power pricing, showing that consumers save up to 40% on their electric bill, compared with 11% using an existing time-of-use rate plan.