A Screen Content (SC) extension to the High Efficiency Video Coding (HEVC) standard has been developed to improve the encoding of SC sequences. SC scenes are rich in repeated patterns, non-noisy regions, sharp-edge areas, and blocks with limited colors, which differ from Natural Content (NC) videos. For the SC Coding (SCC) process, new tools have been incorporated into the HEVC SC extension such as Intra Bock Copy (IBC) and Palette (PLT); these tools improve the compression accuracy at the expense of high computational complexity. In this paper, we present a framework to reduce the encoding time of SC encoders by exploiting the characteristics of the SC blocks. The framework contains two techniques. The first is called Decision Tree Models (DTM), and it includes decision tree-based classification blocks to reduce the number of executed modes. In the DTM technique, the features of each Coding Unit (CU) are extracted and trained to build the classification trees. To further speed up the encoding process, a second technique called Early Splitting Termination (EST) is suggested to stop the normal splitting process of homogeneous blocks by measuring the luminance contrast inside the blocks. Compared with the HM-16.7+SCM-6 reference test model, the proposed framework can provide a 35.96% encoding time reduction on average with only a 0.89% increase in Bjontegaard Delta bit-rate (BD-Rate) under the All-Intra (AI) configuration profile, which outperforms the approaches in the literature. In addition, the proposed framework reduces the encoding time by 54.3% on average for a number of NC sequences recommended for conventional HEVC test, with only 0.74% increment in the BD-Rate. For further speeding up, the proposed scheme has been integrated with an existing approach. Consequently, a 45.84% reduction in time complexity is obtained with a BD-Rate increase of only 1.3%.