Accurate simulation of scatter in projection data of single photon emission computed tomography (SPECT) is computationally extremely demanding for activity distribution in non-uniform dense media. This paper suggests how the computation time and memory requirements can be significantly reduced. First the scatter projection of a uniform dense object (P(SDSE)) is calculated using a previously developed accurate and fast method which includes all orders of scatter (slab-derived scatter estimation), and then P(SDSE) is transformed towards the desired projection P which is based on the non-uniform object. The transform of P(SDSE) is based on two first-order Compton scatter Monte Carlo (MC) simulated projections. One is based on the uniform object (P(u)) and the other on the object with non-uniformities (P(nu)). P is estimated by P = P(SDSE) P(nu)/P(u). A tremendous decrease in noise in P is achieved by tracking photon paths for P(nu) identical to those which were tracked for the calculation of P(u) and by using analytical rather than stochastic modelling of the collimator. The method was validated by comparing the results with standard MC-simulated scatter projections (P) of 99mTc and 201Tl point sources in a digital thorax phantom. After correction, excellent agreement was obtained between P and P. The total computation time required to calculate an accurate scatter projection of an extended distribution in a thorax phantom on a PC is a only few tens of seconds per projection, which makes the method attractive for application in accurate scatter correction in clinical SPECT. Furthermore, the method removes the need of excessive computer memory involved with previously proposed 3D model-based scatter correction methods.