"Arming" only one automation track ?

To record automation from a MIDI source, I press the Overdub button, play start - and automation is recorded. My problem is that all other automation tracks are simultaneously open to record. And the MIDI instrument often sends spurious CC messages: tweaking with the intended knob can produce sufficient vibration to move some other control a notch. Sure, I should get a less worn MIDI instrument - but the budgetary committee denied that motion, so I want a software way.

Is it possible to record MIDI cc for one automation parameter while the others remain untouched, or should I get used to the fact that recording always means recording all automation parameters simultaneously ?