The cost and complexity of deploying measurement infrastructure in the
Internet for the purpose of analyzing its structure and behavior is
considerable.  Basic questions about the utility of increasing the number
of measurements and measurement sites have not yet been addressed which has
lead to a ``more is better'' approach to wide-area measurement studies.  In
this paper, we step toward a more  quantifiable understanding of the
marginal utility of performing  wide-area measurements in the context of
Internet topology discovery.  We  characterize the topology in terms of
nodes, links, node degree distribution, and distribution of end-to-end
flows using statistical and information-theoretic  techniques.  We classify
nodes discovered on the routes between a set of 8 sources and 1277
destinations to differentiate nodes which make up the so called
``backbone'' from those which border the  backbone and those on links
between the border nodes and destination nodes.   This process includes
reducing nodes that advertise multiple interfaces to  single IP addresses.
We show that the utility of adding sources beyond the second source goes
down significantly from the perspective of interface, node, link and node
degree discovery.  We show that the utility of adding destinations is
constant for interfaces, nodes, links and node degree indicating that it is
more important to add destinations than sources.