Warning: Icky. What are these foul-smelling tiny chunks I find at the back of my throat?

It's been going on occasionally for many years...even after brushing and gargling, I will be haunted by the taste of really foul breath at the back of my throat, and a little later a tiny chunk of solid but mushable crud comes up from my throat that smells absolutely awful. I did some research and came up with tonsilloliths, but that sounds like more of a calcified, hard m. Any ideas? It's such an icky thing when it happens and I'd love to prevent it from forming. My tonsils are intact, by the way.