The building on a tree-filled site at Hamilton Street and 11th Avenue was Regina's first city hall, built in 1908. It was a beautiful Romanesque Revival building that was tragically demolished in 1965. In the 1960s, there was little emphasis on preserving heritage buildings. The ill-fated Midtown Centre took its place, later to become the Galleria mall and finally the federal government's offices. I consider the old city hall to be Regina's worst architectural losses.
If the building at Scarth Street and 12th Avenue is the one in the northwest corner (where McCallum Tower I now stands), then you're referring to the McCallum-Hill Building. It was built in 1910, and at ten stories, it was Regina's tallest building for decades. It was demolished in the early 1980s to make way for the aforementioned McCallum tower, the first of the two glass twins.
http://scaa.usask.ca/gallery/regina/...wn_A_1497.html