A small superconducting magnet with a large highly confined field has been designed for ultralow‐temperature cryostats. The magnet provides a central field of 3 T, with a homogeneity of 0.1% over 7.3 mm and negligible hysteresis, while the field at a radial distance of 2 cm is zero. The confinement is accomplished by using the magnet wire itself to simulate the current distribution of a perfect type I superconducting shield.