Interactive medical teleconsultations are an important tool in modern medical practice. Their applications include remote diagnostics, conferences, workshops, and classes for students. In many cases, standard medium or low-end machines are employed, and the teleconsultation systems must be able to provide a high quality of user experience with very limited resources. Particularly problematic are large datasets consisting of image sequences that need to be accessed fluently. The main issue is insufficient internal memory; therefore, proper compression methods are crucial. However, a scenario where image sequences are kept in a compressed format in the internal memory and decompressed onthe-fly when displayed is difficult to implement due to performance issues. In this paper, we present methods for both lossy and lossless compression of medical image sequences that only require compatibility with the Pixel Shader 2.0 standard, which is present even on relatively old, low-end devices. Based on the evaluation of quality, size reduction, and performance, these methods have been proven to be suitable and beneficial for medical teleconsultation applications.