Motivated by dynamic speed scaling, which enables a balance between performance and energy consumption, we got interested in queues in which the server can work at different service speeds and in which the speed of the server can only be changed at arrival instants of an external observer. In the past several works dealt with models in which these type of service speed adaptations occurred. Bekker, Boxma and Resing (2008) studied an M/M/1 queue with a two-stage service rule. Whenever the amount of work in the system is below a threshold the server wants to work at low service speed, otherwise the server wants to work at high service speed. However, speed adaptations can only occur at Poisson instants. The amount of work in the system could either be measured by the number of customers or by the total workload in the system. Later on, the work was extended to the $M/G/1$ workload process, and to Levy processes in Bekker, Boxma and Resing (2009). Here we look at the model in which the server can not only work at two different service speeds but at infinitely many server speeds. When there are $j$ customers in the system, the server wants to work at speed $j$.