Let’s start the joy of apostrophication by forming the possessives of singular nouns! (Of course, the exclamation point is spurious — there is nothing exciting about forming possessives.) First off, there’re three cases that are uncontroversial:

singular nouns not ending in an /s/- or /z/-sound: add ‘s
one fish’s lair – the box’s contents – everybody else’s indignation

plural nouns ending in an /s/- or /z/-sound: add ‘
The Smiths’ misery – the proposals’ results – some boxes’ lids

plural nouns not ending in an /s/- or /z/- sound: add ‘s
laymen’s opinions – geese’s eggs – two fish’s habitats

Snorefest! Let’s get our hands dirty with some controversial possessives! Is it the princess’s diadem or the princess’ diadem? Is Oliver Twist Dickens’s character or Dickens’ character? Was President McKinley Leon Czolgosz’s victim or Leon Czolgosz’ victim? And, lastly, are the Israelites Moses’s or Moses’ people? Let’s check in with some grammarians:

(1) princess’ – Dickens’ – Czolgosz’ – Moses’: a commonly-held belief
(2) princess’s – Dickens’ – Czolgosz’ – Moses’: On the Mark Writing
(3) princess’s – Dickens’s – Czolgosz’ – Moses’: Harold Kolb, James Cochrane, et al
(4) princess’s – Dickens’s – Czolgosz’s – Moses’: Strunk (& White)
(5) princess’s – Dickens’s – Czolgosz’s – Moses’s: Patricia O’Conner

These choices can be translated into the following possible rules for singular possessives:

(1) use ‘s except for nouns ending in s/z
(2) use ‘s except for names ending in s/z
(3) use ‘s except for names where “adding ‘s would make pronunciation difficult” [Brief English Handbook, 292]
(4) use ‘s except for ancient names ending in s/z
(5) use ‘s for all singular nouns

To me, all of these rules are relatively reasonable, though I lean toward (3) and (5) as the best choices. (1) is weird because one pronounces the possessive of princess with the extra -iz sound, so why not write it? (2) is weird for a similar reason; you say Dickens-iz, not just Dickens. (4) requires one to include the time-period of a name, which seems sort of a silly criterion (so you’d have Jesus’ miracles but Jesús’s car), and this probably wouldn’t accurately reflect the phonology of the word. As a result, I think you’re best served to choose between (3) and (5). (3) has the difficulty of being subject to a subjective condition, but generally reflects pronunciation. (5) has the advantage of combining two rules into one. I learned rule (5) when I was a kid, and it’s the one I personally use. However, if you’re worried about how your writing will be perceived by grammar snobs, go with (3). Most of the grammar books I read through pick it. But don’t, unless you pride yourself on being unreasonable, correct someone who handles possessives of singular nouns ending in -s differently from you.

Next up on the apostrophe parade: Possessives for abbreviations!

Summary: The possessive of singular nouns ending in -s is contested. I advise adding ‘s to all of them or at least to those where the suffix doesn’t make it too hard to pronounce. But importantly, there’s some prescriptivist who’ll back up almost any choice of ‘s or ‘, so don’t complain too much about other people’s choices.

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The Preposterous Apostrophes series as it stands: