The first high-pressure neutron diffraction study in a miniature diamond-anvil cell of a single crystal of size typical for X-ray diffraction is reported. This is made possible by modern Laue diffraction using a large solid-angle image-plate detector. An unexpected finding is that even reflections whose diffracted beams pass through the cell body are reliably observed, albeit with some attenuation. The cell body does limit the range of usable incident angles, but the crystallographic completeness for a high-symmetry unit cell is only slightly less than for a data collection without the cell. Data collections for two sizes of hexamine single crystals, with and without the pressure cell, and at 300 and 150 K, show that sample size and temperature are the most important factors that influence data quality. Despite the smaller crystal size and dominant parasitic scattering from the diamond-anvil cell, the data collected allow a full anisotropic refinement of hexamine with bond lengths and angles that agree with literature data within experimental error. This technique is shown to be suitable for low-symmetry crystals, and in these cases the transmission of diffracted beams through the cell body results in much higher completeness values than are possible with X-rays. The way is now open for joint X-ray and neutron studies on the same sample under identical conditions.