Manin's conjecture is known for families of smooth surfaces with a simple conic bundle structure (del Pezzo surfaces of degree 4, Chatelet surfaces). We will generalise the detector approach of these proofs to conic bundles of general shape. This will lead us to consider divisor sums which are much more general than those considered previously. Our applications include lower bounds of the order of magnitude predicted by Manin for families of smooth cubic surfaces with a rational line.