An ideally stiff string has overtones νn, which are sharper than multiples of the fundamental, the inharmonicity being proportional to(n2 − 1). This well known theoretical result has been verified by Schuck and Young [J. Acous. Soc. Am.15, 1, (1943)] for typical strings. It is proposed to improve the tone of a piano string by attaching a small mass, thus lowering the frequency of each normal mode except those for which the mass is at a node. It turns out that for an ideally stiff string, approximate correction of a large number of overtones can be obtained with a single mass suitably located. In the limit of a large mass near the end of the string, the correction is exact for all overtones. A mass of the order of 0.1 g placed a few cm from the end of a typical string adjusts the first eight overtones to within a few hundredths of a semitone, a negligible inharmonicity. Improved tone is expected since the subjective fundamentals derived from difference tones between adjacent partials will show greatly reduced dispersion. The effect of the loading upon tuning would reduced the observed stretching of the octaves to a negligible amount. Deviations from ideal stiffness and the effect of adding two masses are also considered.