Reducing procedures applied to chemical kinetics in Air Pollution Modelling lead to simplified models, whose accuracy is below the classical threshold of $1$ {\%}. The resulting differential-algebraic systems are no stiff but their integration need specific solvers. We propose here an easy to perform algorithm in order to integrate such systems with a low {\small CPU} cost. Comparison is made with some classical solvers such as Euler Backward Implicit ({\small EBI}), {\small QSSA} and the second-order Rosenbrock method {\small ROS2}. This proves the efficiency and the accuracy of the proposed algorithm. We also show that the classical {\small QSSA}-like methods can not be use apart from the framework of reducing procedures, which explains their rather poor accuracy.