Given a metric space
(
X
,
d
)
\left ( {X,d} \right )
we study the existence of an ultrametric
δ
\delta
which is dominated by
d
d
. We give a number of examples and prove, among other results, that such an ultrametric exists if
(
X
,
d
)
\left ( {X,d} \right )
is locally compact and totally disconnected.