Computer technologies make possible virtual reconstructions of ancient structures. In this paper we give a concise overview of the techniques we have used to build a detailed 3D model of the Antonine nymphaeum at the Sagalassos excavation site. These include techniques for 3D acquisition, texture modelling and synthesis, data clean-up, and visualisation. Our aim has been to build a maximally realistic but also veridical model. The paper is also meant as a plea to include such levels of detail into models where the data allow it. There is an ongoing debate whether high levels of detail, and photo-realistic visualisation for that matter, are desirable in the first place. Indeed, detailed models combined with photo-realistic rendering may convey an impression of reality, whereas they can never represent the situation like it really was. Of course, we agree that filling in completely hypothetical structures may be more misleading than it is informative. On the other hand, often good indications about these structures, or even actual fragments thereof, may be available. Leaving out any structures one is not absolutely sure about, combining basic geometric primitives, or adopting copy-and-paste methods - all aspects regularly found with simple model building - also entail dangers. Such models may fail to generate interest with the public and also if they do, may fail to illustrate ornamental sophistication or shape and pattern irregularities.