The design of a "shallow-well" mirror device suitable for production and confinement of an electron cyclotron heated plasma is described. The well is shallow in that the radial variation of the magnetic field strength is ∼ 5%, with a 2:1 axial mirror ratio. The design uses elliptical mirror coils, circular central coils, and straight, skewed quadrupole coils. Coil positions and currents are optimized by finding those combinations which result in the largest axial and radial regions of favourable particle drift. The particle drift direction is determined from the radial gradient of the longitudinal invariant J. The limits on adiabaticity are estimated from the magnetic field gradients. These considerations show that a plasma would be confined with an axial extent of ∼ 160 cm. a radial extent of ∼ 20 cm, and with an adiabatic limit to the electron energy in excess of 5 MeV.