Peyret (1 Fluid Mech., 7 8 , 4 9 4 3 (1976)) and others have described artificial compressibility iteration schemes for solving implicit time discretizations of the unsteady incompressible Navier-Stokes equations. Such schemes solve the implicit equations by introducing derivatives with respect to a pseudo-time variable z and marching out to a steady state in 2. The pseudo-time evolution equation for the pressurep takes the form ap/a7 = -a*V.u, where a is an artificial compressibility parameter and u is the fluid velocity vector. We present a new scheme of this type in which convergence is accelerated by a new procedure for setting a and by introducing an artificial bulk viscosity b into the momentum equation. This scheme is used to solve the non-linear equations resulting from a fully implicit time differencing scheme for unsteady incompressible flow. We find that the best values of a and b are generally quite different from those in the analogous scheme for steady flow (J. D. Ramshaw and V A. Mousseau, Comput. Fluids, 18, 361-367 (1990)), owing to the previously unrecognized fact that the character of the system is profoundly altered by the presence of the physical time derivative terms. In particular, a Fourier dispersion analysis shows that a no longer has the significance of a wave speed for finite values of the physical time step At. Indeed, if one sets a N 1u1 as usual, the artificial sound waves cease to exist when At is small and this adversely affects the iteration convergence rate. Approximate analytical expressions for a and b are proposed and the benefits of their use relative to the conventional values a N (u[ and b = 0 are illustrated in simple test calculations.