Dresser includes a frame having a wall section forming a rear wall, and an upper panel that covers an accessible space. A bracket is designed for attachment to a vertical support, a first connector is attached to the bracket, a second connector is attached to the frame in a position to be in the space and removably engages with the first connector when present in the space under the upper panel. The first and/or second connector is/are length adjustable relative to its supporting structure, i.e., relative to the bracket in the case of the first connector or relative to the frame in the case of the second connector to enable a distance between the frame and the vertical support to be reduced. A reduction in distance between the frame and the vertical support and engagement between the first and second connectors prevents tipping of the piece of furniture.