In speckle velocimetry, Young's fringes observed during analysis of the multiple-exposure photographs of tracer particles seeding a fluid flow are embedded in a speckle noise that renders their analysis difficult. Some first- and second-order statistical properties of this speckle background are considered in this paper. A simple model shows that, because of the small and fluctuating number of scatterers contained in the probe beam, the intensity fluctuations are enhanced, leading to a contrast greater than one. The same model also shows that the speckle grains are not completely independent because of the existence of long-range intensity correlations.