Disclosed are low-profile valve assemblies for engaging a counter top or other mounting surface having a through opening. A special collar is provided which has a flange facing the outer surface of the mounting surface, and a skirt that extends into the through opening where the inward portion of the skirt connects to the valve body. This insets the valve body. o-ring and recess structures are provided to seal the construction, and a handle has an outer skirt to hide the collar.