Regen & Counters

[Hakuu]

When a creature is regen'd do the counters that were on it stay or not?
On a creature such as {Lumberknot}

[Bleakone]

Regenerate causes the lethal damage to not kill it.If something would cause a creature to die that has been regened, the creature taps and is removed from combat with all damage assigned to it removed.

Counters stay. Same with -1/-1 counters. As to why you can't regen once it has enough -1/-1 counters on it cause it comes back and dies anyway