Codec negotiation method, comprising the following steps: 1) a terminal (Ta), called first terminal, belonging to a first IP domain/network, transmits (S1, S'1) at least one message specifying, for a given type of media stream, a list of codecs, called offer Oa, that said first terminal (Ta) is capable of using to communicate with another terminal (Tb), called second terminal, belonging to a second IP domain/network, 2) said message is intercepted (S2, S'2) by a transit device situated on the signalling path between said first and second domains/networks, 3) the transit device determines (S3, S'3) a list of codecs, called adjusted offer Ob, based at least on said offer Oa, 4) the transit device sends (S4, S'4) said adjusted offer Ob to said second terminal (Tb), 5) the second terminal (Tb) determines (S5, S'5) a list of codecs, called response Rb = {Cb, Cb,..., Cb( n)}, comprising n ≥ 1 codecs that are firstly contained in the adjusted offer Ob and secondly such that the second terminal (Tb) is capable of using them, and sends said response Rb to the transit device, and 6) the transit device determines (S6, S'6), based on said response Rb, a list of codecs, called provisional adjusted response R'a, said method being characterized in that it comprises a preliminary step during which a priority list is configured, comprising triplets each formed of: • a codec Ca able to be used by a terminal of the first domain/network, • a codec Cb able to be used by a terminal of the second domain/network, and • a priority degree associated with this pair of codecs (Ca, Cb), and in that said provisional adjusted response is R'a = {Ca, Ca,..., Ca( n)}, where the codec Ca( i), where i = 1,2,..., n, is a codec offering, in association with the codec Cb( i) of the response Rb, the maximum priority degree from among the codecs of the offer Oa. 1) a terminal (Ta), called first terminal, belonging to a first IP domain/network, transmits (S1, S'1) at least one message specifying, for a given type of media stream, a list of codecs, called offer Oa, that said first terminal (Ta) is capable of using to communicate with another terminal (Tb), called second terminal, belonging to a second IP domain/network, 2) said message is intercepted (S2, S'2) by a transit device situated on the signalling path between said first and second domains/networks, 3) the transit device determines (S3, S'3) a list of codecs, called adjusted offer Ob, based at least on said offer Oa, 4) the transit device sends (S4, S'4) said adjusted offer Ob to said second terminal (Tb), 5) the second terminal (Tb) determines (S5, S'5) a list of codecs, called response Rb = {Cb, Cb,..., Cb( n)}, comprising n ≥ 1 codecs that are firstly contained in the adjusted offer Ob and secondly such that the second terminal (Tb) is capable of using them, and sends said response Rb to the transit device, and 6) the transit device determines (S6, S'6), based on said response Rb, a list of codecs, called provisional adjusted response R'a, said method being characterized in that it comprises a preliminary step during which a priority list is configured, comprising triplets each formed of: • a codec Ca able to be used by a terminal of the first domain/network, • a codec Cb able to be used by a terminal of the second domain/network, and • a priority degree associated with this pair of codecs (Ca, Cb), and in that said provisional adjusted response is R'a = {Ca, Ca,..., Ca( n)}, where the codec Ca( i), where i = 1,2,..., n, is a codec offering, in association with the codec Cb( i) of the response Rb, the maximum priority degree from among the codecs of the offer Oa. • a codec Ca able to be used by a terminal of the first domain/network, • a codec Cb able to be used by a terminal of the second domain/network, and • a priority degree associated with this pair of codecs (Ca, Cb),