Load-balanced switch architectures are known to be scalable in both size and speed, which is of interest due to the continued exponential growth in Internet traffic. However, the main drawback of load-balanced switches is that packets can depart out of order from the switch. Randomized load-balancing of application flows by means of hashing on the packet header is a well-known simple solution to this packet reordering problem in which all packets belonging to the same application flow are routed through the same intermediate port and hence the same path through the switch. Unfortunately, this method of load-balancing can lead to instability, depending on the mix of flow sizes and durations in the group of flows that gets randomly assigned to route through the same intermediate port. In this paper, we show that the randomized load-balancing of application flows can be enhanced to provably guarantee both stability and packet ordering by extending the approach with safety mechanisms that can uniformly diffuse packets across the switch whenever there is a build-up of packets waiting to route through some intermediate port. Although simple and intuitive, our experimental results show that our extended randomized load-balancing approach outperforms existing load-balanced switch architectures.