The compression of screen content has attracted the interest of researchers in the last years as the market for transferring data from computer displays is growing. It has already been shown that especially those methods can effectively compress screen content which are able to predict the probability distribution of next pixel values. This prediction is typically based on a kind of learning process. The predictor learns the relationship between probable pixel colours and surrounding texture. Recently, an effective method called `soft context formation' (SCF) had been proposed which achieves much lower bitrates for images with less than 8 000 colours than other state-of-the-art compression schemes. This paper presents an enhanced version of SCF. The average lossless compression performance has increased by about 5% in application to images with less than 8 000 colours and about 10% for images with up to 90 000 colours. In comparison to FLIF, FP8v3, and HEVC (HM - 16.20 + SCM - 8.8), it achieves savings of about 33%, 4%, and 11% on average. The improvements compared to the original version result from various modifications. The largest contribution is achieved by the local estimation of the probability distribution for unpredictable colours in stage II of the compression scheme.