  We show that the breakdown of the Wiedemann-Franz law due to
electron--electron scattering in diffusive spin valves may result in a strong
suppression of the Fano factor that describes the ratio between shot noise and
average current. In the parallel configuration of magnetizations, we find the
universal value $\sqrt{3}/4$ in the absence of a normal-metal spacer layer, but
including the spacer leads to a non-monotonous suppression of this value before
reaching back to the universal value for large spacer lengths. On the other
hand, in the case of an antiparallel configuration with a negligibly small
spacer, the Fano factor is $\sqrt{3 (1-P^2)}/4$, where $P$ denotes the
polarization of the conductivities. For $P\rightarrow \pm 1$, the current
through the system is almost noiseless.
