gistfile1.txt

// public API method
public void someMethod() throws Exception {
  try {
    // some work happens here, maybe not my code
  } catch (final Throwable t) {
    if(t instanceof Exception || t instanceof Error)
      // if t is an Exception or a RuntimeException the method signature already declares it
      // if t is an Error then it is not a checked exception in the first place
      throw UnsafeUtil.unchecked(t);
    else
      // for the case where t happens to be a bare Throwable (e.g. new Throwable(...)) which we would never expect to happen
      throw new InternalError("unexpected Throwable", t);
  }
}

Now, what about the reverse?

// public API method
public void someMethodThatDoesNotThrow() {
try {
// some work happens here, maybe not my code
} catch (final Throwable t) {
if(t instanceof RuntimeException || t instanceof Error)
// if t is a RuntimeException or Error then it is not a checked exception and we can throw it
throw UnsafeUtil.unchecked(t);
else if (t instanceof Exception)
// no alternative but to wrap it
throw new RuntimeException(t);
else
// has to be a bare Throwable (e.g. new Throwable(...)) at this point, which we would never expect to happen
throw new InternalError("unexpected Throwable", t);
}
}