This paper considers the scenario of a flat universe with a network of heavy cosmic strings as the primordial fluctuation spectrum. The joint probability of finding streaming velocities of at least 600 km/s on large scales and local peculiar velocities of less than 800 km/s is calculated. It is shown how the effects of loops breaking up and being born with a spectrum of sizes can be estimated. It is found that to obtain large-scale streaming velocities of at least 600 km/s, it is necessary that either a large value for beta G mu exist or the effect of loop fissioning and production details be considerable.