Félix-Medina and Thompson (2004) proposed a variant of link-tracing sampling in which it is assumed that only a portion of a hidden population, such as drug users or sex workers, is covered by a frame of sites where the members of the population can be found with high probability. A sample of sites is selected and the people on those sites are asked to nominate other members of the population to be included in the sample. We consider this sampling design, and propose several types of Horvitz-Thompson-like estimators of the total and the mean of a response variable, such as monthly drug expenses or number of sexual partners. We also propose Horvitz-Thompson-like estimators of the variances of the estimators of the total and the mean, as well as Wald confidence intervals for these parameters. The results of several simulation studies with real and artificial data indicate that point and interval estimators of the total and mean perform well as long as all the assumptions about the stated models are satisfied and the number of nominees in the portion of the population not covered by the frame is not small, but that their performance deteriorates as the number of nominees decreases. The results also indicate that the proposed estimators are robust to deviations from the model that describes the numbers of people found on the sites, but not to deviations from the assumption that every member of the population has the same probability of being nominated by a particular site. However, in this case, the proposed estimators still yield estimates of the parameters of the correct order of magnitude.