Starting from the flux of particles in a Brownian dynamics simulation we derive boundary conditions, which allow us (i) to couple a Brownian dynamics calculation to a reservoir of particles of a given density, i.e., setting up constant density boundary conditions, and (ii) to build an interface between Brownian dynamics and a diffusional treatment of adjacent simulation volumes. With these algorithms it is sometimes possible to dramatically reduce the system size-and therefore the necessary resources-of multiparticle Brownian dynamics calculations. In this paper we give one-dimensional examples which illustrate potential applications and savings. (C) 2004 American Institute of Physics.