Unemployment benefits, benefit duration, base period and qualifying period are constituent parameters of the unemployment insurance system in most OECD countries. From economic research we know that the amount and duration of unemployment benefits increase unemployment. To analyze the effects of the other two parameters we use a matching model with search frictions and show that there is a trade-off between the qualifying and the base period on the one hand and the amount and duration of the unemployment benefits on the other. A country that combines a high level of unemployment benefits with a long benefit duration can neutralize the effect on the equilibrium rate of unemployment with a long qualifying and/or a short base period.