The excess momentum of a jet in a co-flowing current is shown to be conserved. Using a Lagrangian jet spreading hypothesis, an integral model of the jet in co-flow is formulated and validated against detailed LIF measurements of the concentration field. It is demonstrated that the jet spreading hypothesis using the top-hat velocity as the characteristic velocity can be effectively applied to model the time-averaged jet flow. Theoretical predictions of the jet spreading rate and minimum dilution are in good agreement with experiments. The present results support the applicability of the ‘top-hat’ profile in the integral formulation of buoyant jet in a current. The advantages of the top-hat profile become even clearer for the more complex case of a bent-over jet in crossflow, when the concentration or velocity profile is clearly not Gaussian.