Conservation Agriculture (CA) is a Sustainable Agricultural Intensification strategy based on minimum soil disturbance, permanent soil coverage by living or dead biomass, and diversification of crop rotations. We reviewed the literature on benefits, trade-offs, adoption and adaptation of CA in sub-Saharan Africa (SSA). While CA can improve soils and sustain crop yields, benefits are inconsistent and there are trade-offs with crop residue use, weeds and insect pests, labour demands and short-term yield penalties. Adoption rates by smallholders in sub-Saharan Africa are generally low. We hypothesize that underlying adoption constraints are 1) the magnitude of transformation of management practices required from farmers moving to CA, 2) the multiple inherent trade-offs associated with CA practices and 3) the incompatibility of CA practices to local conditions. We suggest CA adoption in SSA could be improved by focusing the promotion of CA to environments where it best fits, or by facilitating smallholders' adaptation of the practices of CA to respond to their conditions and constraints. We, therefore, propose to move from Conservation Agriculture to Conservation Practices by: (A) identifying and overcoming locally important CA trade-offs through adaptations and complementary practices, and (B) finding farm-specific optimal combinations of practices in terms of feasibility and benefits.