Toilet flushing systems installed in a toilet reservoir. A toilet reservoir stores a fluid that pours into a toilet bowl for carrying waste away from a toilet. Exemplary toilet flushing systems may include a flush sleeve having a sleeve bottom and sleeve top. The exemplary sleeve bottom may connect to a bottom of the toilet reservoir around a reservoir drain. The flush sleeve may be capable of being raised in a raised orientation such that the sleeve top is above the fluid in the toilet reservoir to prevent the fluid from entering the reservoir drain. Exemplary toilet flushing systems may include a flush sleeve actuator that lowers the sleeve top of the flush sleeve below a fluid level in the toilet reservoir to allow the fluid to flow through the flush sleeve into the reservoir drain.