The crystallization of glasses and amorphous solids is studied in many fields to understand the stability of amorphous materials, the fabrication of glass ceramics, and the mechanism of biomineralization. Recent studies have found that crystal growth in organic glasses can be orders of magnitude faster at the free surface than in the interior, a phenomenon potentially important for understanding glass crystallization in general. Current explanations differ for surface-enhanced crystal growth, including released tension and enhanced mobility at glass surfaces. We report here a feature of the phenomenon relevant for elucidating its mechanism: Despite their higher densities, surface crystals rise substantially above the glass surface as they grow laterally, without penetrating deep into the bulk. For indomethacin (IMC), an organic glass able to grow surface crystals in two polymorphs (alpha and gamma), the growth front can be hundreds of nanometers above the glass surface. The process of surface crystal growth, meanwhile, is unperturbed by eliminating bulk material deeper than some threshold depth (ca. 300 nm for alpha IMC and less than 180 nm for gamma IMC). As a growth strategy, the upward-lateral growth of surface crystals increases the system's surface energy, but can effectively take advantage of surface mobility and circumvent slow growth in the bulk.