Functional magnetic resonance imaging (FMRI) has revolutionized the study of linking physical stimuli with localized brain activity. Among the challenges of working with FMRI data, they are noisy, they exhibit spatial correlation, and they are usually large containing tens of thousands of voxels of information. The notion of False Discovery Rate (FDR) has made a great impact on how to perform powerful multiple hypothesis tests to detect signals in such large multivariate data. The spatial dependence in FMRI data requires special care since, if ignored, it can lead to a loss of control of size as well as a deterioration in power of FDR procedures. This article advocates transforming the voxel-wise test statistics to wavelet space, where the coefficients are approximately uncorrelated. We demonstrate, through a series of experiments, that an FDR procedure in wavelet space enhanced by P-value adaptive thresholding (EPAT), maintains control of the size of the multiple-testing procedure and offers substantially increased power over an FDR procedure that is applied directly to the map of (spatially dependent) test statistics. The EPAT methodology, developed here for FMRI data, is generic and can be applied in other dependent data settings.