Adam Sheffer Tel Aviv University We establish an improved upper bound for the number of incidences between m points and n arbitrary circles in three dimensions. The previous best known bound, which applies in any dimension, is O∗(m2/3n2/3+m6/11n9/11+m+n) . Since all the points and circles may lie on a common plane (or sphere), it is impossible to improve the three-dimensional bound without improving the two-dimensional one. Nevertheless, we show that if the set of circles is required to be "truly three-dimensional" in the sense that there exists a q