As you know for your Uniball, not all pencils are the same. A cheap ball pen can have a lot of problems and stop writting at any moment; a cheap pencil has always a broken core or is impossible to sharpen because the wood turns to pulp. But a decent pencil (Tombow Mono 100 or Faber-Castell 9000 or Staedtler Mars) will get you a perfect core and wood from beginning to end that should not break unless you press like crazy. Despite being excelent, they are cheap, about 2€.