There are voice signals from at least two voice sources which are multiplexed by an ATM Adaptation Layer 2 multiplexer (AAL2 MUX) into the same ATM connection after having been processed by a packetizing means such that the AAL2 MUX is presented with assembled AAL2 packets of a suitable periodicity. If the voice data signals are to be compressed, the packetizing means comprises an encoder of a suitable voice codec, e.g. ADPCM, GSM, LD-CELP or CS-ACELP. The voice encoders may also include means for silence removal. The packetizing means further comprises a packetizer, either separated from the voice encoder, or as a part thereof. The packet releases from the packetizing means are synchronized to occur virtually simultaneously. In this way, the released packets from the packetizing means arrive almost simultaneously at the AAL2 MUX, with the result that an ATM cell may be filled with AAL2 packets well before the expiration of the timer Timer-CU of the AAL2 MUX.