Method for managing a plurality of media streams intended to be rendered by a calling device before finalization of set-up of a communication, said method being implemented by said calling device before finalization of set-up of said communication, said method comprising the following steps: sending a communication set-up request to at least one called device, for each media stream of said plurality of media streams: receiving a message associated with said stream in response to the communication set-up request, searching for a first degree of priority associated with said media stream in said message, and obtaining a second degree of priority associated with said media stream depending on the result of the search, selecting a media stream with a view to rendering said media stream, said media stream being selected from said plurality of media streams, depending on the second degrees of priority associated with said media streams of said plurality of media streams, and, rendering the selected media stream, the step of receiving a message further comprising receiving a third message in response to the communication set-up request, and recording, in a memory of the calling device, for a predetermined length of time beginning on receipt of the third message, each stream of said plurality of media streams, said plurality of media streams being received by the calling device, and the selecting step being implemented when the predetermined length of time has elapsed. said method being implemented by said calling device before finalization of set-up of said communication, said method comprising the following steps: sending a communication set-up request to at least one called device, for each media stream of said plurality of media streams: receiving a message associated with said stream in response to the communication set-up request, searching for a first degree of priority associated with said media stream in said message, and obtaining a second degree of priority associated with said media stream depending on the result of the search, selecting a media stream with a view to rendering said media stream, said media stream being selected from said plurality of media streams, depending on the second degrees of priority associated with said media streams of said plurality of media streams, and, rendering the selected media stream, sending a communication set-up request to at least one called device, for each media stream of said plurality of media streams: receiving a message associated with said stream in response to the communication set-up request, searching for a first degree of priority associated with said media stream in said message, and obtaining a second degree of priority associated with said media stream depending on the result of the search, selecting a media stream with a view to rendering said media stream, said media stream being selected from said plurality of media streams, depending on the second degrees of priority associated with said media streams of said plurality of media streams, and, rendering the selected media stream, receiving a message associated with said stream in response to the communication set-up request, searching for a first degree of priority associated with said media stream in said message, and obtaining a second degree of priority associated with said media stream depending on the result of the search, selecting a media stream with a view to rendering said media stream, said media stream being selected from said plurality of media streams, depending on the second degrees of priority associated with said media streams of said plurality of media streams, and, rendering the selected media stream, the step of receiving a message further comprising receiving a third message in response to the communication set-up request, and recording, in a memory of the calling device, for a predetermined length of time beginning on receipt of the third message, each stream of said plurality of media streams, said plurality of media streams being received by the calling device, and the selecting step being implemented when the predetermined length of time has elapsed.