The reduced particle distributions of field-aligned beams observed upstream of the bow shock are examined in detail using Cluster spacecraft. We find that the reduced parallel and perpendicular distribution forms can be strongly geometry-dependent. Above a certain critical value of the angle between the local shock normal and the direction of the magnetic field, $theta$ Bn , the reduced distributions are remarkably well fit by Maxwellians. We have not found any significant changes to the spread in energies for beams at higher values of $theta$ Bn . When the angle $theta$ Bn decreases, leading to smaller beam velocities, a high-energy tail in the distribution appears. When the tail is present, the bulk of the distribution remains Maxwellian. The development of the high-energy tail is well correlated with decreases in the beam speed (or equivalently $theta$ Bn ). Moreover, detailed examination of the angular distributions indicates that particles in the tails of the distributions propagate at significant pitch angles with respect to the magnetic field (are not field-aligned, as are those within the bulk of the distribution) and that these pitch angles are energy-dependent. These new observations do not fit any production mechanism expected at the shock or result from known wave-particle interactions upstream of or within the shock layer.