I tried AMD GPU Clock tool - it appears to be incompatible with the 6970.
MSI Afterburner seems to be a much better product that Trixx, however, it still doesn't reduce the clock below 1375. It allows me to do it, but as soon as I start mining, it reports the speed at 1375.
Also, changing the sliders on Afterburner and/or CCC seems to be a ticklish affair - I will move the slider and one second later it moves back. Is there a way to make sure that only one of the tools is controlling the cards? This happens even if I use task manager to make sure that CCC.exe is not running.