This is the first work to propose a co-design approach for generation of the network model of a convolutional neural network (CNN) and its implementation using the ReRAM technology to achieve power efficiency. State-of-the-art in this area is based on implementation of an already fixed CNN model. It uses parallel crossbar structures to achieve a desired precision quantization of the edge weights using the limited precision provided by individual ReRAM devices. In contrast, in this work we keep the ReRAM crossbar structure in mind during model generation, and target altering a base CNN model such that the resulting implementation will be more power efficient. This is by means of eliminating the parallel crossbars as much as possible, thus reducing the number of required analog-to-digital and digital-to-analog converters which are dominant sources of power consumption. We study four architectural techniques which are applicable to convolutional or fully-connected layers in a CNN to alter the network model, thus enabling it to work with lower precision of the weights with negligible loss in accuracy. In our experiments, we achieve at least 50% power savings with almost no loss in accuracy for popular CNNs compared to ReRAM implementation of the base model. Further, we propose 2 independent power reduction techniques and investigate the impact of replacing the conventional analog Sigmoid activation function with a simpler design in digital mode on power. The results show that the power consumption of the network can be further decreased to at least 30% of the base model.