Morton recorded this tune (often misspelled as Milenburg joys) in 1924 with the New Orleans Rhythm Kings, but copyright is from 1925.
Morton seems to keep getting the credit... but the main theme was written by Paul Mares and Leon Roppolo. They used to play it at informal gigs up along Lake Pontchartrain in their teens; it was a variation on the well known changes of one of the themes of "Tiger Rag". They called it "Golden Leaf Strut", after a brand of marijuana cigarette they were fond of (reefers were still legal in Louisiana in those days).
A few years later Mares and Roppolo were up in Chicago playing with the New Orleans Rhythm Kings (NORK). They were making a series of recordings for Gennett. According to Joe Mares, Morton was then plugging tunes for the Melrose Brothers publishers; the Melroses advised Morton to see if he could get the popular Rhythm Kings to record some of his compositions. Morton already knew Mares, who liked Morton's "London Blues" and "Mr. Jelly Lord" and agreed to record them. Morton was invited to a rehersal to help arrange his pieces for the NORK. While there he also contributed arrangement ideas to some other tunes in the NORK repertory. Morton added an introduction to "Golden Leaf Strut" (which it was decided to rename "Milenberg Joys" for recording and publication). Morton and the NORK hit it off so well that he was invited to sit in with the band for the recording session.

It's interesting that many bands play the tune without the introduction (the part Morton wrote), but credit the tune to Morton. If played without the introduction, Milneberg Joys should properly be credited to Paul Mares and Leon Roppolo. (Roppolo's grandson told that the family still gets royalties.)

The song was to be named after a resort area on Lake Pontchartrain called Milneburg. Milneburg was named after Alexander Milne, a Scotsman who emigrated to New Orleans in 1776. Being an astute business man he bought up much of the property around the lake and the area was called Milneburg. It had hundreds of camps where all of the New Orleans jazz musicians played at one time or another. Milne wound up as one of New Orleans first millionaires and donated almost all of his money to charities in and around New Orleans.

Much of what was called Milneburg early in the first third of this century was actually in Lake Pontchartrain. The buildings and dock walkways connecting them were on wooden pilings in the shallows of the lake. It was indeed a very important area for music. It was very popular for dances and parties every weekend of New Orleans long summer, and even important in being a place where, in those days of racial segregation being mandated by law, musicians on different sides of the Jim Crow barrier had extended chances to listen to eachother and informally jam. Milneburg was at the end of Elysian Fields Avenue. An early steam railway was put on this thouroghfare connecting the city by the river to the lake some 5 miles away in the 1830s. It was officially called the Pontchartrain Rail Road, but the early 20th century New Orleanians refered to the line by the nickname of the archaic steam engine, "Smoky Mary".

The Lake Pontchartrain shorefront of New Orleans was extended by dredgeing and the construction of seawalls, filling in what had been Milneburg. The location of the center of old Milneburg is now underneath the present University of New Orleans campus.