Internet of Things (IoT) devices and applications are being deployed in our homes and workplaces and in our daily lives. These devices often rely on continuous data collection and machine learning models for analytics and actuations. However, this approach introduces a number of privacy and efficiency challenges, as the service operator can perform arbitrary inferences on the available data. Recently, advances in edge processing have paved the way for more efficient, and private, data processing at the source for simple tasks and lighter models, though they remain a challenge for larger, and more complicated models. In this paper, we present a hybrid approach for breaking down large, complex deep neural networks for cooperative, privacy-preserving analytics. To this end, instead of performing the whole operation on the cloud, we let an IoT device to run the initial layers of the neural network, and then send the output to the cloud to feed the remaining layers and produce the final result. We manipulate the model with Siamese fine-tuning and propose a noise addition mechanism to ensure that the output of the user's device contains no extra information except what is necessary for the main task, preventing any secondary inference on the data. We then evaluate the privacy benefits of this approach based on the information exposed to the cloud service. We also asses the local inference cost of different layers on a modern handset. Our evaluations show that by using Siamese fine-tuning and at a small processing cost, we can greatly reduce the level of unnecessary, potentially sensitive information in the personal data, and thus achieving the desired trade-off between utility, privacy and performance.