A computer-implemented method for providing access to private computer networks, the method comprising the steps of: receiving (405,440), under control of a computing system for a configurable network service that provides a programmatic interface for use by multiple clients to configure private computer networks for use by the multiple clients, first information that is programmatically provided by a first client via the programmatic interface to configure a first private computer network for use by the first client, the first private computer network including a group of multiple of a plurality of computing nodes provided by the configurable network service, the multiple computing nodes each being configured to be associated with at least one of multiple network addresses specified in the first information for use with the first private computer network; obtaining (405, 470), under control of the computing system, second information to configure access from the first private computer network to a subset of computing-related resources that are associated with a namespace within a network-accessible remote resource service, the second information including an identifier associated with the namespace within the remote resource service; automatically, under control of the computing system, configuring the first private computer network to enable access from the multiple computing nodes to the subset of computing- related resources provided by the remote resource service, the configuring including associating the identifier with an indicated one of the multiple network addresses that represents the remote resource service, so that communications sent to the remote resource service via the indicated network address to access the subset of computing-related resources are modified to include an indication of the identifier for use by the remote resource service in identifying the namespace; and initiating, under control of the computing system, availability of access to the first private computer network from one or more remote computing systems of the first client. receiving (405,440), under control of a computing system for a configurable network service that provides a programmatic interface for use by multiple clients to configure private computer networks for use by the multiple clients, first information that is programmatically provided by a first client via the programmatic interface to configure a first private computer network for use by the first client, the first private computer network including a group of multiple of a plurality of computing nodes provided by the configurable network service, the multiple computing nodes each being configured to be associated with at least one of multiple network addresses specified in the first information for use with the first private computer network; obtaining (405, 470), under control of the computing system, second information to configure access from the first private computer network to a subset of computing-related resources that are associated with a namespace within a network-accessible remote resource service, the second information including an identifier associated with the namespace within the remote resource service; automatically, under control of the computing system, configuring the first private computer network to enable access from the multiple computing nodes to the subset of computing- related resources provided by the remote resource service, the configuring including associating the identifier with an indicated one of the multiple network addresses that represents the remote resource service, so that communications sent to the remote resource service via the indicated network address to access the subset of computing-related resources are modified to include an indication of the identifier for use by the remote resource service in identifying the namespace; and initiating, under control of the computing system, availability of access to the first private computer network from one or more remote computing systems of the first client.