We propose a magnetic domain wall (DW) oscillator scheme, in which a low dc current excites gigahertz angular precession of a DW at a fixed position. The scheme consists of a DW pinned at a magnetic anisotropy step in a perpendicularly magnetized nanostrip. The frequency is tuned by the current flowing through the strip. A perpendicular external field tunes the critical current density needed for precession, providing great experimental flexibility. We investigate this system using a simple one-dimensional model and full micromagnetic calculations. This oscillating nanomagnet is relatively easy to fabricate and could find application in future nanoscale microwave sources. © 2011 American Institute of Physics.