A preliminary design for a B-factory has been made using asymmetric collisions between positrons in the Positron-Electron Project (PEP) storage ring and electrons in a new, low-energy ring. The design utilizes small-aperture, permanent-magnet quadrupoles close to the interaction point (IP). Optimization of optical and beam parameters at the IP is discussed, as well as the lattice design of the interaction region and of the rings. The preliminary design for a 12 GeV*2 GeV B-factory, called Apiary I, gives the rather modest luminosity of 0.5*10/sup 33/ cm/sup -2/ s/sup -1/. A major limitation was the power that can be absorbed by the PEP vacuum chamber. It is suggested that, by going to a more symmetrical system such as 9 GeV*3 GeV, it may be possible to go to a luminosity that is almost a factor of four higher.<>