Current velocity model building techniques have been developed specifically with parallel geometry in mind. In this geometry it is possible to create common-offset gathers, to migrate individual gathers, and then to analyse moveout in the image gathers directly as a function of offset. In practice, well-sampled 3D common-offset gathers with constant azimuth are not available, at least in land data acquired with the orthogonal geometry or other crossed-array techniques, and not even in data acquired with the parallel geometry. Therefore, alternative data gathers have to be sought which are suitable for migration and which still allow migration velocity analysis. The method proposed in this paper is based on an extension of the notion of a minimal data set, being a single-fold alias-free data set, suitable for migration. Examples of minimal data sets are cornmon-offset gathers with constant azimuth and cross-spreads. However, proper minimal data sets cannot always be constructed, or, in other cases, minimal data sets do not extend across the entire survey area. This requires the construction of pseudo-minimal data sets. Each pseudo- minimal data set is an approximation of a minimal data set; their number should be equal to the fold count. In parallel geometry the pseudo-minimal data sets are still close to common-offset gathers. These gathers can be used directly for velocity analysis. In other geometries, the pseudo-minimal data sets encompass a wide range of offsets. Then it is necessary to determine from all traces in a pseudo-minimal data set which trace is the imaging trace, and what is its offset. A possible technique to determine this offset is the vector-weighted diffraction stack. The proposed data gathering and velocity-analysis technique needs further research and testing for the best results.