Both the successful determination of the entrainment rate and the calculation of initial values are important aspects of the Patankar-Spatding (P-S) method since they are critical for the attainment of accurate solutions. A new scheme for calculating the entrainment rate, which is very stable and nearly problem-independent, is presented. Here, the main x dependence of the entrainment rate is estimated by using global Quantities known at the previous x step; in particular, it is found to vary inversely with the boundary-layer thickness. This estimation is adjusted by a coefficient which varies very slowly with x and which is determined by a fixed-point method. In addition, a method is given which lets the actual PS computer program generate its own initial values with desired accuracy. Finally, a new explicit formula for the transverse velocity is derived; the formula makes it possible to calculate this velocity component in a very simple manner, using only information already available as part of the solution.