  We give upper bounds for the number of rational points of bounded
anti-canonical height on del Pezzo surfaces of degree at most five over any
global field whose characteristic is not equal to two or three. For number
fields these results are conditional on a conjecture relating the rank of an
elliptic curve to its conductor, while they are unconditional in positive
characteristic. For quartic or quintic del Pezzo surfaces with a conic bundle
structure, we establish even stronger estimates unconditionally as long as the
characteristic is not two.
