To make an informed choice about whether to be screened, people need information that allows them to weigh up the benefits and harms of screening. To understand their screening test results they require even more information. Yet currently, people attending a screening programme or considering a screening test may only be told that the test can detect disease or risk factors for disease, and that early intervention improves outcomes. When given their test results, people are generally only told the test was abnormal ("positive") or normal ("negative"). We believe that information given before and after the screening test can, and should, be improved. This will probably require information that includes both the benefits and harms of screening and is probabilistic. Indeed, we believe the traditional dichotomisation of screening test results into positive and negative is problematic, and could be replaced by standard use of risks or probabilistic data before and after screening. The relevant risk data could be explained in a range of ways, for example, quantitatively, qualitatively, and/or by "anchoring" to everyday experiences. In this paper we explore why dichotomisation of screening test results is problematic and look at the adverse consequences of presenting test results in terms of true and false, positive and negative. We present some ideas on alternative ways of providing information on screening programmes and screening test results. Our aim is to stimulate debate about these issues and to provide some starting points which could be further developed and evaluated in a wide range of screening programmes.