The present invention concerns methods and compositions involving the production or generation of siRNA mixtures or pools capable of triggering RNA-mediated interference (RNAi) in a cell. Compositions of the invention include kits that include reagents for producing or generating siRNA pools. The present invention further concerns methods using polypeptides with RNase III activity for generating siRNA mixtures or pools that effect RNAi, including the generation of a number of RNA molecules to the same target gene.