Odd-primary homotopy exponents of compact simple Lie groups Donald M. Davis and Stephen D. Theriault 57T20, 55Q52 math.AT/0601441 Davis, Lehigh Univ., Bethlehem, PA 18015, dmd1@lehigh.edu Theriault, Univ. of Aberdeen, Aberdeen AB243UE, U.K., s.theriault@maths.abdn.ac.uk We note that a recent result of the second author yields upper bounds for odd-primary homotopy exponents of compact simple Lie groups which are often quite close to the lower bounds obtained from v1-periodic homotopy theory.