Thank you all for the very valuable information! I've come to the conclusion that I may not be using enough solder. I know you shouldn't use too much, but I'm thinking that's my problem.
Speaking of problems, I was trying to solder a ring shank and attempted about 3 times and my solder simply refused to flow. I made every effort to make my joint as flush as possible with no gaps (previous pieces joined with no problems despite not having a perfect join.) But no matter how even I tried to heat it, my solder just blackened. I usually apply my flux and my solder and then heat because I can't just use a solder pick and put it on the joint as I'm heating. My hands shake too much and I'm not Coordinated enough. If I heat the piece for a few seconds first then stop and apply solder, I sometimes run into problems there too.
So when doing a ring, should I heat slightly, then add my solder or try again the way I was before? (Flux, solder then heat?)