Recently, researchers have been increasingly interested in collecting personal network data. Collecting this type of data is particularly burdensome on the respondents, who need to elicit the names of alters, answer questions about each alter (network composition), and evaluate the strength of possible relationships among the named alters (network structure). In line with McCarty et al.'s (2007) research, we propose reducing respondent burden by randomly sampling a smaller set of alters from those originally elicited. Via simulation, we assess the estimation error we incur when measures of the network structure are computed on a random sample of alters and illustrate the trade-offs between reduction in respondent burden (measured with the amount of interview time saved) and total estimation error incurred. Researchers can use the provided trade-offs figure to make an informed decision regarding the number of alters to sample when in need to reduce respondent burden.