The control charts are main tools of statistical surveillance of quality in production processes. Exponentially weighted moving average charts that make use of exact control limits are discussed in detail in this paper. We start by assessing the impact of the smoothing constant \lambda not only in the in-control average run length (ARL) of upper one-sided EWMA charts with exact control limits, but also in the range of the exact control limits of such charts with a common in-control ARL value (i.e. matched in-control). Based on the analytical results and on an extensive simulation study we conclude that the out-of-control ARL of matched in-control upper one-sided EWMA charts with exact control limits increases with \lambda. This in turn suggests the use of \lambda values as close to the zero as possible and motivates what we called the (upper one-sided) limit chart. Its performance is extensively studied with regard to the ARL. Finally, we investigate the impact of \lambda on the ARL of EWMA charts with asymptotic control limits; the (maximum) conditional average delay is also addressed as an additional performance measure.