A network device has a processor to control message traffic between the network device and other devices in a network, a port to allow the network device to send and receive the message traffic and a transcompression element to receive indicators of compression renegotiation messages and to transmit indicators of compression renegotiation acknowledgement, as well as perform compression/decompression. A method of controlling compression in a network receives an indicator of compression renegotiation at a decompressor on a first network device, and transmits an indicator of compression renegotiation acknowledgement to a compressor element on a second network device. Another method of controlling compression in a network determines if a compression method for outgoing data is compatible with a decompression method for incoming data. If the compression and decompression methods are compatible, incoming data is transmitted as outgoing data without compression or decompression, with monitoring of message traffic for any compression renegotiation messages. Compression/decompression may be performed after compression renegotiation or may be ceased.