After you've used up all your Unique, you might try some Hodgdon's Universal Clays. It's a lot cleaner, and shoots just as well with equivalent powder charges.
Nothing against Unique, but Universal is pretty darned good.
As my supply of Unique was starting to run a bit low, on your advice I ordered some Hodgdon Universal. I haven't had opportunity to try it in the .44 yet, but I shot 50 rounds of .38s loaded with it earlier this afternoon (158 gr coated lead SWC over 4.5 gr Universal) and I was very pleased with how clean it shot. Much cleaner than the same bullet using 4.7 gr of Unique. I like it. Looking forward to trying it in the .44. Thanks for the advice!