This invention provides trace address compression by comparing respective bytes of a current trace address with a stored prior trace address. Only the least significant bytes of the current trace address that do not match the stored prior trace address or are less significant than any section of the current trace address that does not match the stored prior trace address are transmitted. This sometimes reduces the amount of data that needs to be transmitted. The prior trace address may be updated with the current trace address if there is a complete mismatch.