The CMC should go first near the antenna feedpoint. Even that might not be enough.
If you have an antenna farm connected to an antenna switch, or sharing a common ground panel / back of rig, you may also have the equivalent of many "common mode verticals", where a CMC right after the switch to the loop is beneficial too. But start with one at the feedpoint.
That's one test I do after building loops - test them as the SOLE antenna directly to the radio. Then, attach all your other gear (if you have it) and test again - any loss of directionality or weirdness can mean that the common-mode from all the other antennas is swamping your loop, and additional choking / grounding measures should be investigated.
If you have an antenna farm connected to an antenna switch, or sharing a common ground panel / back of rig, you may also have the equivalent of many "common mode verticals", where a CMC right after the switch to the loop is beneficial too. But start with one at the feedpoint.
That's one test I do after building loops - test them as the SOLE antenna directly to the radio. Then, attach all your other gear (if you have it) and test again - any loss of directionality or weirdness can mean that the common-mode from all the other antennas is swamping your loop, and additional choking / grounding measures should be investigated.