By combining droplet based single cell transcriptomics with CRISPR-Cas based perturbations we demonstrate an approach that will allow researchers to perform thousands of genetic manipulations in a single pooled experiment. This pooled approach represents an approximate 10 fold improvement in cost over current methods. By increasing the number of cells per droplet we demonstrate that for a small reduction in sensitivity for differentially expressed genes that decrease in expression we gain an additional increase in sample size. Finally, by randomly lentivirally integrating several sgRNAs in each cell, we show the ability to extend the method to perform combinatorial screens. The random structure of the experimental design matrix, so constructed, satisfies the incoherence properties in a compressed sensing framework. Together, these statistical and experimental methods will enable researchers to perform large scale screening of perturbations, including systematic dissection of epistatic effects, using RNA transcription as a phenotype.