In multiple hypothesis testing, there’s often structure in the decisions made about individual observations. Take a gene expression study where the expressions of n genes are collected over m tissues, hypotheses about individual observations, such as whether a gene is associated with a genetic variation in two similar tissues are often related. Standard procedures often answer these questions about groups of observations by considering the contexts independently. However, there often exists information in the groups, for example an individual gene is probably associated with a genetic variation in two similar tissues. In order to fully account for this information, a procedure must make decisions about the observations in a group simultaneously. We propose a method, called the multidimensional discovery procedure (MDP) that optimally make these simultaneous decisions by performing joint hypothesis tests within a group. MDP is optimal in the sense that it maximizes the expected true positives for a fixed level of expected false positives.