Deep Neural Networks trained on large datasets can be easily transferred to new domains with far fewer labeled examples by a process called fine-tuning. This has the advantage that representations learned in the large source domain can be exploited on smaller target domains. However, networks designed to be optimal for the source task are often prohibitively large for the target task. This is especially problematic when the network is to be used in applications with limited memory and energy requirements. In this work we address the compression of networks after domain transfer. We focus on a special class of compression algorithms based on low-rank matrix decomposition. Existing methods base compression solely on learned network weights and ignore the statistics of network activations. We show that domain transfer leads to large shifts in network activation rates and that it is desirable to take this into account when compressing. We demonstrate that considering activation statistics when compressing weights leads to a rank-constrained regression problem with a closed-form solution. Because our method takes into account the target domain, it can more optimally remove the redundancy in the weights; it removes weights only relevant to the source domain while keeping weights crucial to the target domain. Experiments show that our Domain Adaptive Low Rank (DALR) method significantly outperforms existing low-rank compression techniques. With our approach, the fc6 layer of VGG19 can be compressed more than 4x more than using truncated SVD alone – with only a minor loss in accuracy. When applied to domain-transferred networks it allows for compression down to only 5-20% of the original number of parameters with only a minor drop in performance.