Pruning is one of the mainstream methods to compress over-parameterized neural networks, resulting in significant practical benefits. Recently, another line of work has explored the direction of fusion, i.e. merging, independently trained neural networks. Here, we seek to marry the two approaches in a bid to combine their advantages into a single approach, which we term `Intra-Fusion'. Specifically, we implicitly utilize the pruning criteria to result in more informed fusion. Agnostic to the choice of a specific neuron-importance metric, Intra-Fusion can typically prune an additional considerable amount of the parameters while retaining the same accuracy as the standard pruning approach. Additionally, we explore how fusion can be added to the pruning process to significantly decrease the training time while maintaining competitive performance. We benchmark our results for various networks on commonly used datasets such as CIFAR10, CIFAR100, and ImageNet. More broadly, we hope that the proposed approach invigorates exploration into a fresh alternative to the predominant compression approaches.