['Cooperation is ubiquitous in biological systems, yet its evolution is a long lasting evolutionary problem. A general and intuitive result from theoretical models of cooperative behaviour is that cooperation decreases when its costs are higher, because selfish individuals gain selective advantage.', 'Contrary to this intuition, we show that cooperation can increase with higher costs. We analyse a minimal model where individuals live on a lattice and evolve the degree of cooperation. We find that a feedback establishes between the evolutionary dynamics of public good production and the spatial self-organisation of the population. The evolutionary dynamics lead to the speciation of a cooperative and a selfish lineage. The ensuing spatial self-organisation automatically diversifies the selection pressure on the two lineages. This enables selfish individuals to successfully invade cooperators at the expenses of their autonomous replication, and cooperators to increase public good production while expanding in the empty space left behind by cheaters. We show that this emergent feedback leads to higher degrees of cooperation when costs are higher.'] Does high cost enhance cooperation through the interplay between evolution and self-organisation?