Eradicating disease from livestock populations involves the balancing act of removing sufficient numbers of diseased animals without removing too many healthy individuals in the process. As ever more tests for bovine tuberculosis (BTB) are carried out on the UK cattle herd, and each positive herd test triggers more testing, the question arises whether 'false positive' results contribute significantly to the measured BTB prevalence. Here, this question is explored using simple probabilistic models of test behaviour. When the screening test is applied to the average UK herd, the estimated proportion of test-associated false positive new outbreaks is highly sensitive to small fluctuations in screening test specificity. Estimations of this parameter should be updated as a priority. Once outbreaks have been confirmed in screening-test positive herds, the following rounds of intensive testing with more sensitive, albeit less specific, tests are highly likely to remove large numbers of false positive animals from herds. Despite this, it is unlikely that significantly more truly infected animals are removed. BTB test protocols should become based on quantified risk in order to prevent the needless slaughter of large numbers of healthy animals.