We present recent improvements in assembly-level calculations for reactor analysis, including modifications that support core-level analysis by quasi-diffusion. Our main focus is on accurately approximating the effects that neighboring assemblies have on the few-group cross sections, assembly discontinuity factors, form factors, and other transport parameters of a given assembly. We show that we can do this by using albedo boundary conditions that are estimated with low computational cost. We also present an efficient way to tabulate these effects to permit accurate interpolation by the core-level algorithm. We describe our algorithms and present results from several difficult test problems containing mixed-oxide and UO2 assemblies. Our methodology significantly reduces the largest errors made by present-day methodology. For example, in our test problems it reduces the maximum pin-power error by a factor of ~5.