All honeybees use the waggle dance to recruit nestmates. Studies on the dance precision of Apis mellifera have shown that the dance is often imprecise. Two hypotheses have been put forward aimed at explaining this imprecision. The first argues that imprecision in the context of foraging is adaptive as it ensures that the dance advertises the same patch size irrespective of distance. The second argues that the bees are constrained in their ability to be more precise, especially when the source is nearby. Recent studies have found support for the latter hypothesis but not for the "tuned-error" hypothesis, as the adaptive hypothesis became known. Here we investigate intra-dance variation among Apis species. We analyse the dance precision of A. florea, A. dorsata, and A. mellifera in the context of foraging and swarming. A. mellifera performs forage dances in the dark, using gravity as point of reference, and in the light when dancing for nest sites, using the sun as point of reference. Both A. dorsata and A. florea are open-nesting species; they do not use a different point of reference depending on context. A. florea differs from both A. mellifera and A. dorsata in that it dances on a horizontal surface and does not use gravity but instead "points" directly toward the goal when indicating direction. Previous work on A. mellifera has suggested that differences in dance orientation and point of reference can affect dance precision. We find that all three species improve dance precision with increasing waggle phase duration, irrespective of differences in dance orientation, and point of reference. When dancing for sources nearby, dances are highly variable. When the distance increases, dance precision converges. The exception is dances performed by A. mellifera on swarms. Here, dance precision decreases as the distance increases. We also show that the size of the patch advertised increases with increasing distance, contrary to what is predicted under the tuned-error hypothesis.