Got the blobs, need help

Hi, I'm a long time property manager and the bane of my existence is the blob of solder left in a sweat fitting after removing a component. The one that really got me today was a reducing Tee 3/4 X 1/2 X 3/4. The 1/2 had to have the component removed and there is a small blob of solder sitting on the bottom of the horizontal 1/2 inch arm so the new piece won't fit without removing the blob. I have used a number of things to remove the sloder, heat and pick with a brush, use my pocket knife to scrape out the solder, I've even tried to get a 1/2' reamer but this fitting is next to an adjoining pipe and so I can't get in. Even though I've done it sometimes by fluxing real well and then heating, sliding the new piece in and adding solder I am always afraid that I may have a void and it will eventually leak. So how do you pro's do it????

Wiping with a dry rag, and a 1/2 round bastard file will finish it off.

To remove the blob heat the pipe then wipe it with a dry rag... Done!