Rectangular or exponential current pulses of duration congruent-to 0.1 mus traversing a Bloch wall are found to induce wall displacements DELTAx less-than-or-equal-to 10 mum/pulse in a Ni81Fe19 film of thickness congruent-to 263 nm. The critical current density for wall displacement is j(c) congruent-to 1.35 X 10(6) A/cm2, about 20-200 times lower than for Neel or cross-tie walls investigated earlier. Wall motion arises probably from the precession of wall spins under the influence of the ''s-d exchange torque'' exerted by conduction electrons crossing the wall. The low j(c) value and easy precession of spins in a Bloch wall reflect the very small value congruent-to 300 muT of the wall demagnetizing field which opposes spin orientation out of the wall plane in films of this thickness. A dc in-plane hard-axis field causes a linear decrease of j(c). A dc easy-axis field smaller than H(c) produces only a very slow decrease of j(c).