Texture bombing is a texture synthesis approach that saves memory by stopping short of assembling the output texture from the arrangement of input texture patches; instead, the arrangement is used directly at run time to texture surfaces. However, several problems remain in need of better solutions. One problem is improving texture diversification. A second problem is that mipmapping cannot be used because texel data is not stored explicitly. The lack of an appropriate level-of-detail (LoD) scheme results in severe minification artefacts. We present a just-in-time texturing method that addresses these two problems. Texture diversification is achieved by modelling a texture patch as an umbrella, a versatile hybrid 3-D geometry and texture structure with parameterized appearance. The LoD is adapted continuously with a hierarchical algorithm that acts directly on the arrangement map. Results show that our method can model and render the diversity present in nature with only small texture memory requirements.