Existing calculations of the Leslie coefficients for rigid rods endowed with the Maier-Saupe potential are here extended to investigate the consequences of relaxing the constraint of a complete molecular rigidity. In particular, the recently proposed model of the Slightly Bending Rod (SBR) is used to calculate the ratio alpha3/alpha2, the sign of which controls whether the nematic is of the tumbling or flow-aligning type. The results show that SBRs are more prone to tumbling than fully rigid rods. The flow-aligning to tumbling transition, which takes place by increasing the order parameter (e.g. by decreasing the temperature) is shifted, for SBRs, to a smaller value of the order parameter.