Social inequalities constitute a major obstacle to the social and economic cohesion of a country, particularly those affecting the health field. In the field of cancer screening, the current situation is that of a social gradient of participation and strong territorial inequalities. This paper reports on the results of two interventional investigations to add incentives to the existing device to provide screening tests for specific populations. A prospective trial with a collective randomization unit was set up from April 2011 to April 2013 in the 3 areas of Northern France (Aisne, Oise and Somme), to assess social workers' help with screening of colorectal cancer (Prado trial). A retrospective study was conducted on the experience of mammobile driving in the area of Orne for several years. The analysis of the results shows that each of these devices is capable of reducing or even erasing social and territorial inequalities at a reasonable cost to society. It also shows that in terms of screening, inequalities can only be reduced if additional devices dedicated to particular populations are added to the national system according to a principle of proportionate universalism.