A stream (1) of media frames (12-16, 22-26, 32-36) is generated by providing multiple media frames (22-26) having respective assigned default timestamps (40) defining rendering times of the media data of the media frames (22-26) according to a default rendering time schedule. Respective alternative timestamps (50) are assigned to at least a portion of the media frames (22-26). These alternative timestamps (50) define alternative rendering times of the media data of the media frames (22-26) according to an alternative rendering time schedule. The alternative timestamps (50) can be used for providing an efficient media rendering when tuning in to the stream (1) at an intermediate position of a frame grouping (20) of the media frames (22-26) thereby missing some of the media frames (22, 24) of the frame grouping (20).