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Traditionally, deep convolutional neural networks consist of a series of convolutional and pooling layers followed by one or more fully connected (FC) layers to perform the final classification. While this design has been successful, for datasets with a large number of categories, the fully connected layers often account for a large percentage of the network's parameters. For applications with memory constraints, such as mobile devices and embedded platforms, this is not ideal. Recently, a family of architectures that involve replacing the learned fully connected output layer with a fixed layer has been proposed as a way to achieve better efficiency. In this paper we examine this idea further and demonstrate that fixed classifiers offer no additional benefit compared to simply removing the output layer along with its parameters. We further demonstrate that the typical approach of having a fully connected final output layer is inefficient in terms of parameter count. We are able to achieve comparable performance to a traditionally learned fully connected classification output layer on the ImageNet-1K, CIFAR-100, Stanford Cars-196, and Oxford Flowers-102 datasets, while not having a fully connected output layer at all.