Up joke

When you top somebody's joke with another joke.

"Dick went to the doctor’s the other day
Did Dick?
Dick Did!
Poorly Dick?
Sick Dick!"

Such an up joke.

-- Ugly Dave Gray and Graham Kennedy

"Dick was dining at the restaurant.
Dick was?
Was Dick ever! It was on the tax-payer!
Clever Dick.
Slick Dick!"

Double up joke.

-- Ugly Dave Gray and Graham Kennedy