Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the transit times of the void between axially placed detectors, determined from in-core neutron noise measurements. In order to determine a realistic velocity profile which shows an inflection point and hence has to be at least a third order polynomial, one needs four transit times and hence five in-core detectors at various axial elevations, whereas the standard instrumentation usually consists only of four in-core detectors. Attempts to determine a fourth transit time by adding a TIP detector to the existing four LPRMs and cross-correlate it with any of the LPRMs have been unsuccessful so far. In this paper we thus propose another approach, where the TIP detector is only used for the determination of the axial position of the onset of boiling. By this approach it is sufficient to use only three transit times. Moreover, with another parametrisation of the velocity profile, it is possible to reconstruct the velocity profile even without knowing the onset point of boiling, in which case the TIP is not needed, although at the expense of a less flexible modelling of the velocity profile. In the paper the principles are presented, and the strategy is demonstrated by concrete examples, with a comparison of the performance of the two different ways of modelling the velocity profile. The method is tested also on velocity profiles supplied by system codes, as well as on transit times from neutron noise measurements.