Addition strategies used by 36 kindergarten children were examined. Children were given written stimuli (such as "2+5" and "3+7") during two sessions taking place a week apart. Results indicated that once children came to rely on mental addition strategies, they often quickly invented more economical procedures to compute sums. Also confirmed was the hypothesis that a specific mental addition strategy recently discovered in a case study (counting-all starting with the larger addend) was not an uncommon labor-saving device among young children. On the other hand, the strategy of counting-on from the first addend was found to be relatively rare as a result of its being cognitively less economical than either counting-all starting with the larger addend or counting-on from the larger addend. A double count model of mental addition explained the above results. Finally, several devices that may help children make the transition from counting-all to counting-on were observed. (Author/MP)