Fast earthward plasma flows are commonly observed in the magnetotail plasma sheet. These flows are often termed as bursty bulk flows because of their bursty nature, and they are considered to be generated by magnetic reconnection. Close to the neutral sheet (B-x similar to 0), the fast flows are considered to be associated with an enhanced dawn-to-dusk electric field (E-y > 0), which together with the northward magnetic field component (B-z > 0) protrude the plasma earthward via enhanced E x B-drift. Sometimes, reversals in the dawn-dusk velocity component perpendicular to the magnetic field (V-perpendicular to y) are measured in association with B-x sign changes in the flows. This suggests that the electric field component in the north-south direction (E-z) can play a role in determining the dawn-dusk direction of the enhanced drift. We present data measured by the Magnetospheric Multiscale, which demonstrate that E-z can have a dictating role for V-perpendicular to y of fast flows. Furthermore, it is shown that the critical contribution of E-z is not limited only to V-perpendicular to y, but it can also dominantly determine the enhanced drift of the fast flows in the X direction (V-perpendicular to x). The latter can occur also near and at the neutral sheet, which adds an alternative configuration to the conventional picture of E-y and B-z being the main players in driving the earthward fast flows. The domination of E-z in the studied events appears with potential signatures of an influence of a nonzero dawn-dusk component of the interplanetary magnetic field (IMF B-y) on the magnetotail.