Many recent self-supervised frameworks for visual representation learning are based on certain forms of Siamese networks. Such networks are conceptually symmetric with two parallel encoders, but often practically asymmetric as numerous mechanisms are devised to break the symmetry. In this work, we conduct a formal study on the importance of asymmetry by explicitly distinguishing the two encoders within the network -- one produces source encodings and the other targets. Our key insight is keeping a relatively lower variance in target than source generally benefits learning. This is empirically justified by our results from five case studies covering different variance-oriented designs, and is aligned with our preliminary theoretical analysis on the baseline. Moreover, we find the improvements from asymmetric designs generalize well to longer training schedules, multiple other frameworks and newer backbones. Finally, the combined effect of several asymmetric designs achieves a state-of-the-art accuracy on ImageNet linear probing and competitive results on downstream transfer. We hope our exploration will inspire more research in exploiting asymmetry for Siamese representation learning.