How do you use possessives in front of gerunds?

English speakers and writers sometimes puzzle over what to do with nouns or pronouns that come before gerunds.
Informal: I appreciated Jane helping us clean up the mess. (noun)
More acceptable: I appreciated Jane's helping us clean up the mess. (possessive noun)
Informal: Ron's parents did not approve of him getting married. (personal pronoun)
More acceptable: Ron's parents did not approve of his getting married. (possessive adjective)

Although the noun/pronoun + gerund combination is not uncommon and would make sense to most English speakers, editors and writing teachers generally recommend using a possessive before a gerund.