1. A method for compressing a data stream comprising pictures with static regions and non-static regions, the method comprising: detecting a static region in a picture; modifying a quantization parameter (QP), over successive pictures, of regions that remain static in the successive pictures, the QP being changed in accordance with a multi-step change from a start QP to a target QP over the successive pictures until a non-static region is detected, the QP being changed in accordance with a set of improvement levels and each one of the improvement levels is associated with a quantization parameter, wherein each one of the regions is located at a same location as the static region as detected, wherein modifying the QP comprises: determining a current improvement level for the static region of a given picture based on a number of successive pictures comprising the static regions that precede the given picture; associating the current improvement level with the static region of the given picture; and retrieving a corresponding quantization parameter to compress the static region of the given picture; and interrupting the modifying of the quantization parameter when the non-static region is detected and applying a regular QP thereto.