 We have proposed three new measures of shared information, unique information, and synergistic information for two random variables, yz, when conditioned on a third random variable, x. These measures are based on the idea of unique information, which states that shared and unique information should depend solely on the marginal distributions of the pairs, x, y, x, z, and yz. In addition, these measures satisfy an important invariance property, meaning they are bounded by any other measures that also satisfy this property. We then compared these measures to other candidate measures and found that they provide useful insights into the relationship between shared, unique and synergistic information. This article was authored by Nils Burt Schinger, Johannes Rau, Eckhart Ulbricht, and others.