Narrow spaces and passages are not a rare encounter in cultural heritage, the shape and extension of those areas place a serious challenge on any techniques one may choose to survey their 3D geometry. Especially on techniques that make use of stationary instrumentation like terrestrial laser scanning. The ratio between space extension and cross section width of many corridors and staircases can easily lead to distortions/drift of the 3D reconstruction because of the problem of propagation of uncertainty. This paper investigates the use of fisheye photogrammetry to produce the 3D reconstruction of such spaces and presents some tests to contain the degree of freedom of the photogrammetric network, thereby containing the drift of long data set as well. The idea is that of employing a multi-camera system composed of several fisheye cameras and to implement distances and relative orientation constraints, as well as the pre-calibration of the internal parameters for each camera, within the bundle adjustment. For the beginning of this investigation, we used the NCTech iSTAR panoramic camera as a rigid multi-camera system. The case study of the Amedeo Spire of the Milan Cathedral, that encloses a spiral staircase, is the stage for all the tests. Comparisons have been made between the results obtained with the multi-camera configuration, the auto-stitched equirectangular images and a data set obtained with a monocular fisheye configuration using a full frame DSLR. Results show improved accuracy, down to millimetres, using a rigidly constrained multi-camera.