Except Rwanda. The Rwandan DHS shows an unusual pattern in which unmet need (as defined by women who do not want to get pregnant and are not using contraception) declined by nearly a half between 2005 and 2010, to which the authors credit the invigoration of a national family planning program. Contraceptives use more than doubled between 2005 and 2010. This stands in stark contrast to other sub-Saharan countries (e.g. Ghana, Burkina Faso, Kenya and Nigeria) where use of contraceptives has basically stalled since the mid-1990s.
What this paper doesn't answer is how the drivers of unmet need (e.g. lack of knowledge of contraceptive methods and supply; low quality and limited availability of family planning services; cost of methods in travel and time; familial objections and concerns about acceptability) that are propping up that green curve, can be fixed.