The growing number of devices using the wireless spectrum makes it important to find ways to minimize interference and optimize the use of the spectrum. Deep learning models, such as convolutional neural networks (CNNs), have been widely utilized to identify, classify, or mitigate interference due to their ability to learn from the data directly. However, there have been limited research on the complexity of such deep learning models. The major focus of deep learning-based wireless classification literature has been on improving classification accuracy, often at the expense of model complexity. This may not be practical for many wireless devices, such as, internet of things (IoT) devices, which usually have very limited computational resources and cannot handle very complex models. Thus, it becomes important to account for model complexity when designing deep learning based models for interference classification. To address this, we conduct an analysis of CNN based wireless classification that explores the trade-off amongst dataset size, CNN model complexity, and classification accuracy under various levels of classification difficulty: namely, interference classification, heterogeneous transmitter classification, and homogeneous transmitter classification. Our study, based on three wireless datasets, shows that a simpler CNN model with fewer parameters can perform just as well as a more complex model, providing important insights into the use of CNNs in computationally constrained applications.