Most national health surveys do not permit precise measurement of the health of racial/ethnic subgroups that comprise <1 per cent of the U.S. population. We identify three potentially promising sample design strategies for increasing the accuracy of national health estimates for a small target subgroup when used to supplement a small probability sample of that group and apply these strategies to American Indians/Alaska Natives (AI/AN) and Chinese using National Health Interview Survey data. These sample design strategies include (1) complete sampling of targets within households, (2) oversampling selected macrogeographic units, and (3) oversampling from an incomplete list frame. Stage (1) is promising for Chinese and AI/AN; (2) works for both groups, but it would be more cost-effective for AI/AN because of their greater residential concentration; (3) is somewhat effective for groups like Chinese with viable surname lists, but not for AI/AN. Both (2) and (3) efficiently improve measurement precision when the supplement is the same size as the existing core sample, with diminishing additional returns as the supplement grows relative to the core sample, especially for (3). To avoid large design effects, the oversampled geographic areas or lists must have good coverage of the target population. To reduce costs, oversampled geographic tracts and lists must consist primarily of targets. These techniques can be used simultaneously to substantially increase effective sample sizes (ESSs). For example, (1) and (2) in combination can be used to multiply the nominal sample size of AI/AN or Chinese by 8 and the ESS by 4.