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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 an algorithm that solves the problem of finding, at any renegotiation, the parameters for a RVBR service when the knowledge of the input traffic is limited to the next interval (local optimisation problem). 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. Keywords: Shaping system, renegotiation, VBR parameters, resources optimisation, RSVP.