During last years, new applications needing more requirements have been developed, and their requirements have boosted the search for what we know as Quality of Service, QoS. To provide QoS, diverse formulas have been studied. Among them, there are the call admission control algorithms (CAC) and the usage parameters control algorithms (UPC). In networks that support QoS, a call admission control (CAC) algorithm determines whether or not a new traffic flow can be admitted to the network such that all users will receive their performance. Such an algorithm is a key component of multi-service networks as it determines the extent to which network resources are utilized and whether the promised QoS parameters are actually delivered. In this paper, a new lightweight algorithm, the Two Tests algorithm, is presented. This new proposal requires neither intense use of CPU to make decisions nor a complex traffic characterization, as opposed to other well-known algorithms, such as the Equivalent Capacity algorithm. Evaluation has been performed through simulation by using the OPNET [1] environment, and considering CBR (Constant Bit Rate) traffic and VBR (Variable Bit Rate) traffic based on MPEG-2 video traces. It is shown that, when compared to the well-known Equivalent Capacity algorithm, the Two Tests algorithm is able to make a more effective admission control, at a fraction of its computational cost.