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When building Deep Learning (DL) models, data scientists and software engineers manage the trade-off between their accuracy, or any other suitable success criteria, and their complexity. In an environment with high computational power, a common practice is making the models go deeper by designing more sophisticated architectures. However, in the context of mobile devices, which possess less computational power, keeping complexity under control is a must. In this paper, we study the performance of a system that integrates a DL model as a trade-off between the accuracy and the complexity. At the same time, we relate the complexity to the efficiency of the system. With this, we present a practical study that aims to explore the challenges met when optimizing the performance of DL models becomes a requirement. Concretely, we aim to identify: (i) the most concerning challenges when deploying DL-based software in mobile applications; and (ii) the path for optimizing the performance trade-off. We obtain results that verify many of the identified challenges in the related work such as the availability of frameworks and the software-data dependency. We provide a documentation of our experience when facing the identified challenges together with the discussion of possible solutions to them. Additionally, we implement a solution to the sustainability of the DL models when deployed in order to reduce the severity of other identified challenges. Moreover, we relate the performance trade-off to a new defined challenge featuring the impact of the complexity in the obtained accuracy. Finally, we discuss and motivate future work that aims to provide solutions to the more open challenges found., Pre-print. Accepted and to be published in WAIN@ICSE 2021