How to remove clicks from audio... when joining video clips with VirtualDub?

[any ANONYMOUS forum user]

I use the VirtualDub video editing software a lot, and I've been cutting between extremely short clips (only 5 frames each) very fast. Whenever I make a cut, there's always a click between the audio from the first clip and the second click. Is there any way I can remove or prevent this from happening so the audio sounds clearer?

The same thing happens when I splice audio clips together in Audacity, unless I fade out each individual track before.
The clicks don't appear on the waveform, so Click Removal from Audacity won't work. I can only hear the clicks, but I can't see them.