My preferred "Freddie, don't whine" method has been to just ignore. It seems that whenever I acknowledge his "pay attention to me" noises, even with just a "stop" or a "no" he just continues louder. He's eventually learned that I will be back and that he is fine in his "safe space," whether that be his crate for sleeping, or the kitchen (gated) for longer periods of alone time (or little time outs). It seems to be working.
My breeder told me never to come to him when he cried, and so far that's worked. The only time I acknowledge his whining is when it seems like he wants to go outside (although we are working on another signal), or when he wakes up in the morning (though today I beat him to it!).