In the Wee Small Hours was created in 1955-04.

In the Wee Small Hours of the Morning was created on 1955-02-17.

The phrase is "in the small hours" (of the night) or more poetically "the wee small hours of the morning". This simply applies to the first hours of the day, after midnight, as the ones with the lowest clock numbers.
Sometimes it's "the wee hours". In either case the words "of night" are implied. The hours after midnight have small numbers: one o'clock, two o'clock and three o'clock. They are therefore called "small hours" or "wee hours".

The phrase is "in the small hours" (of the night) or more poetically "the wee small hours of the morning". This simply applies to the first hours of the day, after midnight, as the ones with the lowest clock numbers.
Sometimes it's "the wee hours". In either case the words "of night" are implied. The hours after midnight have small numbers: one o'clock, two o'clock and three o'clock. They are therefore called "small hours" or "wee hours".

In the Wee Wee Hours... was created in 1987.