Observations of several protostellar jets show systematic differences in radial velocity transverse to the jet propagation direction, which have been interpreted as evidence of rotation in the jets. In this paper we discuss the origin of these velocity shifts, and show that they could be originated by rotation in the flow, or by side to side asymmetries in the shock velocity, which could be due to asymmetries in the jet ejection velocity/density or in the ambient medium. For typical poloidal

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... velocities (~ 100-200 km/s), an asymmetry >~ 10% can produce velocity shifts comparable to those observed. We also present three dimensional numerical simulations of rotating, precessing and asymmetric jets, and show that, even though for a given jet there is a clear degeneracy between these effects, a statistical analysis of jets with different inclination angles can help to distinguish between the alternative origins of transverse velocity shifts. Our analysis indicate that side to side velocities asymmetries could represent an important contribution to transverse velocity shifts, being the most important contributor for large jet inclination angles (with respect the the plane of the sky), and can not be neglected when interpreting the observations.