Probabilistic tractography methods that use Monte Carlo sampling of voxelwise fibre orientation probability density functions suffer from distance-related artefacts due to the propagation of uncertainty along the tract path. These are manifested as a preferential weighting of regions close to the tracking start point at the expense of more distant regions--an effect that can mask genuine anatomical connections. We propose a methodology based on comparison of the conventional connection probability map with a null connection map that defines the distribution of connections expected by a random tracking process and that is dominated by the same distance effects. When the connection probability is significantly greater than the result of the null tracking result this identifies voxels where the diffusion information is providing more evidence of connection than that expected from random tracking. We show that the null connection probability map used is governed by Poisson statistics within each voxel, allowing analytical estimation of connection values that are significantly different to the null connection values. The resultant significant connection maps can be combined with the conventional probabilistic tractography output to produce maps of significant connections which reduce distance-related artefacts by removing areas where the observed frequency of connection is dominated simply by distance effects and not the diffusion information. This is achieved by applying an objective statistical interpretation of observed patterns of connection which cannot be achieved by simple thresholding of conventional probabilistic tractography maps due to the distance effect.