As with the Hertz theory, the Johnson-Kendall-Roberts (JKR) theory of the elastic contact of spheres with adhesion uses the parabolic approximation for the profile of the sphere which is only valid for small contact radii. Recent experiments on adhesion of small particles on soft elastic substrates have revealed that the contact radius under zero load can be rather large and does not vary as the particle radius to the 2/3 power. The JKR theory is extended by using the exact expression for the profile of the sphere and the results are in good agreement with published experiments.