Nanocrystalline Fe-M-B (M = Zr or Nb) alloys (Nanoperm) exhibit excellent soft magnetic properties when M content is 6–7 at%. Lowering the M content below 4 at% usually results in a coarsening of the nanocrystallites and so sets a lower limit on the M content for Nanoperm. In this report we have demonstrated that a highly refined, magnetically soft nanostructure can be achieved for Fe-Nb-B-(Cu) alloys with a Nb content well below 4 at% by employing a rapid annealing process which utilises a heating rate of 150 K s⁻¹. The low Nb-content of these nanocrystalline alloys brings about a high saturation magnetic polarization of 1.85–1.9 T, well above the upper limit of Nanoperm (1.7 T). These newly developed, bcc-Fe based nanocrystalline soft magnetic alloys which have an M content lower than 4 at% are named HiB-Nanoperm. HiB-Nanoperm exhibits excellent soft magnetic properties with a coercivity as low as 2.5 A m⁻¹ and a high initial permeability of ∼10⁴ at 1 kHz. A possible explanation for the rapid annealing induced grain refinement observed for this Fe-M-B system is that the higher annealing temperatures used by this process bring about a lowering of the precursor amorphous phase viscosity which then triggers homogeneous nucleation, thereby considerably increasing the number density of bcc-Fe nucleation sites.