AbstractHigh population compliance is seen as a prerequisite for an equitable screening service. To achieve high compliance fixed appointments are usually advocated. However, the costs of achieving high compliance have not previously been described. To assess the costs of achieving high compliance we have used a randomised trial of two common appointment methods: 800 women aged 45‐49 living within 20 miles of Aberdeen were selected at random from the Community Health Index. They were randomly assigned to receive one of two letters—one offering a fixed appointment, the other inviting them to telephone to make an appointment.For a defined population fixed appointments achieved high compliance but only by reducing the opportunities for screening; for every 100 women screened, 110 additional women were denied the opportunity of a screening test. In contrast the open letters of invitation achieved efficiency by increasing the number of women screened with given resources within a larger population. Thus for screening services with fixed budgets, high compliance is achieved only by screening fewer peo