A shaper is a system that stores incoming bits in a buffer and delivers them as early as possible, while forcing the output to be constrained with a given arrival curve. A shaper is time invariant if the traffic constraint is defined by a fixed arrival curve; it is time varying if the condition on the output is given by a time varying traffic contract. This occurs, for example, with renegotiable variable bit rate (RVBR) services. We focus on the class of time varying shapers called time varying leaky bucket shapers; such shapers are defined by a fixed numbers of leaky buckets, whose parameters (rate and bucket size) are changed at specific transition moments. We assume that the bucket levels are kept unchanged at those transition moments (no reset'' assumption). Our main finding is an input-output characterisation for this class of time varying shapers. Then we apply it to the tradeoff in optimising the RVBR service, assuming that a perfect prediction of future traffic can be made. We provide two algorithms that solve the problem of finding, at any renegotiation, the parameters for a RVBR service, respectively when the knowledge of the input traffic is limited to the next interval (local optimisation problem) and when we dispose of the complete input traffic description (global optimisation problem). We compare, by means of simulation, the two resulting algorithms to study the validity of the local approach. We illustrate the impact of the no-reset'' assumption by analyzing on some examples the losses that occur when the source chooses the opposite approach, namely, the ``reset'' approach. Furthermore we simulate the RVBR service versus the nenegotiable constant bit rate (RCBR) service and illustrate that the RVBR approach can provide substantial benefits. Finally, we discuss the impact of the size of the renegotiation interval on the efficiency of the RVBR service.