Most standard tomographic inversion methods require many measurements with a regular coverage of the object studied. A new method has been developed to obtain tomographic reconstructions from measurements by systems with a small number of detectors and an irregular coverage. The method reconstructs values on a regular grid in projection space from the measurements on an irregular grid by an iterative interpolation scheme. It applies a priori information and smoothing between the iterations. Furthermore, consistency of the results is obtained by an iteration between projection space and actual space. The tomographic reconstructions required in this iteration are made by a filtered-back-projection (FBP) method for the regular grid. The algorithm has been tested on assumed emission profiles. For a fan-beam system with a limited number of views the method has been compared with an FBP method for fan-beam systems; it was found to perform equally well. The method has also been applied to the visible-light tomography system on the RTP tokamak, which has only 80 channels and a very irregular coverage. Satisfactory results were obtained both for simulations and for reconstructions of actual measurements. The method appears to be a promising new approach to tomographic reconstructions of measurements by systems with irregular coverage and a small number of detectors.