Demand Side Management (DSM) is a popular approach for grid-aware peak-shaving. The most commonly used DSM methods either have no look ahead feature and risk deploying flexibility too early, or they plan ahead using predictions, which are in general not very reliable. To counter this, a DSM approach is presented that does not rely on detailed power predictions, but only uses a few easy to predict characteristics. By using these characteristics alone, near optimal results can be achieved for electric vehicle (EV) charging, and a bound on the maximal relative deviation is given. This result is extended to an algorithm that controls a group of EVs such that a transformer peak is avoided, while simultaneously keeping the individual house profiles as flat as possible to avoid cable overloading and for improved power quality. This approach is evaluated using different data sets to compare the results with the state-of-the-art research. The evaluation shows that the presented approach is capable of peak-shaving at the transformer level, while keeping the voltages well within legal bounds, keeping the cable load low and obtaining low losses. Further advantages of the methodology are a low communication overhead, low computational requirements and ease of implementation.