A recent trend in functional magnetic resonance imaging is to test for association of clinical disorders with every possible connection between selected brain parcels. We investigated the impact of the resolution of functional brain parcels, ranging from large-scale networks to local regions, on a mass univariate general linear model (GLM) of connectomes. For each resolution taken independently, the Benjamini–Hochberg procedure controlled the false-discovery rate (FDR) at nominal level on realistic simulations. However, the FDR for tests pooled across all resolutions could be inflated compared to the FDR within resolution. This inflation was severe in the presence of no or weak effects, but became negligible for strong effects. We thus developed an omnibus test to establish the overall presence of true discoveries across all resolutions. Although not a guarantee to control the FDR across resolutions, the omnibus test may be used for descriptive analysis of the impact of resolution on a GLM analysis, in complement to a primary analysis at a predefined single resolution. On three real datasets with significant omnibus test (schizophrenia, congenital blindness, motor practice), markedly higher rate of discovery were obtained at low resolutions, below 50, in line with simulations showing increase in sensitivity at such resolutions. This increase in discovery rate came at the cost of a lower ability to localize effects, as low resolution parcels merged many different brain regions together. However, with 30 or more parcels, the statistical effect maps were biologically plausible and very consistent across resolutions. These results show that resolution is a key parameter for GLM-connectome analysis with FDR control, and that a functional brain parcellation with 30 to 50 parcels may lead to an accurate summary of full connectome effects with good sensitivity in many situations.