In much primary pressure-volume and acoustic thermometry in the range 2.5-27 K appreciable benefit could be expected from smoothing the slopes of the isotherms and refitting them with the smoothed slopes. Since the isotherms are generally few in number, it is desirable to find a realistic form for the temperature dependence of the corresponding virial coefficients which has only two or three undetermined coefficients. The commonly suggested form, a + bT −1 + δ(T), δ(T) being a small single term adjustment, is investigated on the basis of the direct and exchange 4He phase shift sums, G+(k) and G−(k), given by Boyd, Larsen and Kilpatrick (BLK). It is shown that only a limited region of the G+(k) curve contributes significantly to the value of B(T) for most of the range of interest and that this has a particularly simple form leading to the terms a + bT −1. But, as BLK found, this is of insufficient accuracy to represent B(T) over the full range. In order to extend its usefulness two small but significant calculated corrections are proposed, one to allow for the effect of the exchange phase shift sum G−(k) and one to compensate for ignoring low momentum features of the direct sum G+(k). A plausible, but somewhat arbitrary, form for δ(T), cT −1/2, is also deduced from the G+(k) curve, though, having inserted the two corrections, it makes only a small contribution to the smoothing procedure. From these considerations recommendations for smoothing thermometry isotherm slopes are deduced and assessed numerically. It is found that they can considerably enhance the quality of all but the finest work. They also facilitate the derivation of acoustic virial coefficients from pressure-volume virial coefficients and vice versa. The indirect dependence of the recommendations on the obsolete Lennard-Jones potential on which BLK based their phase shifts is argued to be inconsequential.