  Madden has shown that in contrast to the situation with frames, the smallest
dense quotient of a $\kappa$-frame need not be Boolean. We characterise these
so-called d-reduced $\kappa$-frames as those which may be embedded as a
generating sub-$\kappa$-frame of a Boolean frame. We introduce the notion of
the closure of a $\kappa$-frame congruence and call a congruence clear if it is
the largest congruence with a given closure. These ideas are used to prove
$\kappa$-frame analogues of known results concerning Boolean frame quotients.
In particular, we show that d-reduced $\kappa$-frames are precisely the
quotients of $\kappa$-frames by clear congruences and that every $\kappa$-frame
congruence is the meet of clear congruences.
