A falling (“declarative”) nuclear pitch accent has a simple shape: an upward pitch obtrusion on the accented syllable, a fairly abrupt fall to near the bottom of the speaker's range, and a more gradual fall to the end. The synthesis algorithm in Anderson, Pierrehumbert, and Liberman (1983) decomposes this pattern into a H* pitch accent followed by an L phrase accent and an L boundary tone. It devotes four parameters to the realization of the H* accent (amount of rise, target F0 height, target duration, target time) and two parameters to the L phrase accent (target F0, target time). The parameters depend in part on properties of the accented syllable (e.g., prominence) and in part on characteristics of larger phrases (e.g., pitch range). The resulting time/F0 pairs are subject to interpolation and smoothing. This paper improves on the naturalness of the algorithm by incorporating findings from a recent study by Steele. In particular, the principles that determine the timing, magnitude, and alignment of the H* F0 rise and of the H* to L F0 fall have been improved.