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Delivery of real time streaming applications, such as voice and video over IP, in packet switched networks is based on dividing the stream into packets and shipping each of the packets on an individual basis to the destination through the network. The basic implicit assumption on these applications is that shipping all the packets of an application is done, most of the time,over a single path along the network. In this work, we present a model in which packets of a certain session are dispersed over multiple paths, in contrast to the traditional approach. The dispersion may be performed by network nodes for various reasons such as load-balancing, or implemented as a mechanism to improve quality, as will be presented in this work. To study the effect of packet dispersion on the quality of voice over IP (VoIP) applications,we focus on the effect of the network loss on the applications, where we propose to use the Noticeable Loss Rate (NLR) as a measure (negatively) correlated with the voice quality. We analyze the NLR for various packet dispersion strategies over paths experiencing memoryless (Bernoulli) or bursty (Gilbert model) losses,and compare them to each other. Our analysis reveals that in many situations the use of packet dispersion reduces the NLR and thus improves session quality. The results suggest that the use of packet dispersion can be quite beneficial for these applications.