This work introduces Directed-Evolution (DE) method for sparsification of neural networks, where the relevance of parameters to the network accuracy is directly assessed and the parameters that produce the least effect on accuracy when tentatively zeroed are indeed zeroed. DE method avoids a potentially combinatorial explosion of all possible candidate sets of parameters to be zeroed in large networks by mimicking evolution in the natural world. DE uses a distillation context [5]. In this context, the original network is the teacher and DE evolves the student neural network to the sparsification goal while maintaining minimal divergence between teacher and student. After the desired sparsification level is reached in each layer of the network by DE, a variety of quantization alternatives are used on the surviving parameters to find the lowest number of bits for their representation with acceptable loss of accuracy. A procedure to find optimal distribution of quantization levels in each sparsified layer is presented. Suitable final lossless encoding of the surviving quantized parameters is used for the final parameter representation. DE was used in sample of representative neural networks using MNIST, FashionMNIST and COCO data sets with progressive larger networks. An 80 classes YOLOv3 with more than 60 million parameters network trained on COCO dataset reached 90% sparsification and correctly identifies and segments all objects identified by the original network with more than 80% confidence using 4bit parameter quantization. Compression between 40x and 80x. It has not escaped the authors that techniques from different methods can be nested. Once the best parameter set for sparsification is identified in a cycle of DE, a decision on zeroing only a sub-set of those parameters can be made using a combination of criteria like parameter magnitude and Hessian approximations.