When do you use an extra apostrophe “s” following a last name ending with the letter “s”?

When do you use an extra apostrophe “s” following a last name ending with the letter “s”?

Chicago Manual of Style, 14th Edition, 6.24-30 says:

The general rule for the possessive of nouns covers most proper nouns, including most names ending in sibilants (but see exceptions in 6.26-27 and alternatives in 6.30). Kansas’s; Burns’s poems; Marx’s theories; Dickens’s novels….For names ending in silent s, z, or x the possessive, unlike the plural, can generally be formed in the usual way without suggesting an incorrect pronunciation: Margaux’s bouquet; Descartes’s works.

Traditional exceptions to the general rule for forming the possessive are the names Jesus and Moses: in Jesus’ name; Moses’ leadership…”How to form the possessive of polysyllabic personal names ending with the sound of s or z,” says CMS, “probably occasions more dissension among writes and editors than any other orthographic matter open to disagreement.”

Gregg Reference Manual, 7th Edition, Sabin, 631 says:

To form the possessive of a singular noun that ends in an “s” sound, be guided by the way you pronounce the word: (a) if a new syllable is formed in the pronunciation of the possessive, add an apostrophe plus “s,” e.g., Mr. Morris’s eyeglasses; Miss Knox’s hairdo; Mrs. Lopez’s term paper…(b) If the addition of an extra syllable would make a word ending in an “s” hard to pronounce, add the apostrophe only, e.g., Mrs. Phillips’ comment; Mr. Hastings’ bike…

There will always be controversy on this “style” issue, since some style guides call for only an apostrophe followed by the letter “s.” Some are more concerned with the way a word looks in print, others with the way it sounds when spoken.