Built in 1969 (with about 188 units) as French Quarter and featuring top-tier features, including elevators (it had three-story apartment buildings), marble vanities, and thick carpeting, 6505 Westheimer was one of the better apartments in the Westheimer and continued to be into the mid-1970s, now known as Hillcroft House, advertising as being adjacent to the "Magic Circle", an early term for what is now Uptown. This carried into the next name of the apartments, as in 1976, it was known as Magic Circle Apartments. By 1979, the apartments were being renovated, despite being only a decade old and going through two name changes.
Sometime in the early 1980s, it was renamed as Westheimer Gardens Apartments. In the mid-1980s, it fell back into the hands of Ronald Marr, who briefly owned it in the early 1970s. The apartment complex was largely occupied by Salvadoran immigrants who worked at the nearby restaurants, and Marr originally had plans to do basic fix up and continue it, but economically it wouldn't work out, as it would push the rent higher than what could tenants could pay. Instead, Marr went all ahead in a full rehabilitation. The buildings were shored up with dozens of new steel beams, covered parking was reinstalled (previously torn down in rent reduction), and the courtyard areas were improved with new landscaping, units were improved (including adding Jacuzzi tubs), along with introducing the Water Mill Social and Health Club. In 1987, the apartments re-debuted as The Water Mill. Today, Water Mill Apartments is not quite as nice as what it was over twenty years ago, but it hasn't changed names since.
Sources: "A success story in apartments", Houston Chronicle 1/28/88, additional articles and advertisements