Hindbrains of sedated, prone, suckling rats were irradiated 11-13 days postpartum horizontally from the left with an array of upright wiggler-generated synchrotron X-ray microbeams spaced either 105 or 210 μm apart. The microbeams were in an array of 48 (for the 205 μm interval) or of 96 (for the 105 μm interval), with microbeam widths ranging from 19 to 39 μm, the array having an approximately 1-cm-square cross section. The microbeams imparted doses of either ≈50 or ≈150 Gy to the inner skin (computed here as the average dose 0.5–1.5 mm deep to the surface of our phantom) at their entrance to the head, where their median energy was ≈120 keV. The array traversed the postero-superior quadrant of the phantom, which represented the occiput of the head, so that about one in five photons in the array bypassed the head altogether. The resultant radiation doses to the head were simulated by computing the tracks of thirty billion X-ray photons incident on the multislit collimator along with all ≥1 keV secondary electrons from interactions in water of the photons entering the left circular wall of the 1.00 cm-radius, 1.55 cm-wide (i.e., "15.5 mm-long") cylindrical head phantom. The computations were performed using the Los Alamos National Laboratory Monte Carlo radiation transport computer program MCNPX, yielding ionization energies imparted to approximately twenty-four thousand 1.00 mmdeep, 10 μm-wide, up to 3.33 mm-high voxels distributed throughout one quadrant of the phantom, each representing up to 33.3 μg water. Computed nadir doses between microbeams were defined as the average of the three lowest doses between horizontally adjacent peak doses. We notice that nadir interbeam doses under 5 Gy were associated with neurologically minor and/or inconsequential sequelae fifteen months after irradiation and thus postulate that unidirectional microbeam radiosurgery using hindbrain nadir doses under 5 Gy may safely ameliorate the symptoms of some presently intractable human infantile neuraxial malignancies.