at least not use the more subtle forms ("tricks" )of Compulsion on him. And Rand is resistant to Alanna's attempts to Compel him via the Warder Bond (although this is not conclusively proven to have anything to do with him holding saidin).

LOC
Threads Woven of Shadow

She used Compulsion so often like a hammer that one might forget that she could wield the weaker forms of it with great delicacy, twisting a mind’s path so subtly that even the closest examination might miss every trace of her. In fact, she might have been the best at that who ever lived.
He let the gateway vanish but held on to saidin; those tricks did not work on someone wrapped in the Source.

Sammael actually thinks anyone holding the Power is immune to the more subtle forms of Compulsion.

Later it's proven that at least when the stronger forms of Compulsion are used a channeler embracing the Source is not immune to the stronger weaves.

TPoD
New Alliances

She had spun the nets strong, for anger’s sake, nearly strong enough to do harm, and the women stood staring at her adoringly, eyes wide and mouths hanging open in adulation, intoxicated with worship. They were hers to command, now. If she told them to cut their own throats, they would. Suddenly Graendal realized that Moghedien was no longer embracing the Source. This much Compulsion might have shocked her into letting go.

seems obvious that strong Compulsion can overpower the "immunity"


Emphasis mine.