A tandem packer (100) seals a wellbore annulus with first and second seals. The packer has a body defining a bore therethrough and has a shoulder disposed on the body. A compressible element (150) is disposed on the body adjacent the shoulder. A piston is movably disposed on the body adjacent the compressible element and is activated by fluid pressure communicated through a port in the packer's bore. When actuated, the piston fits between the compressible element and the body to initially expand it outward. With further fluid pressure, the piston compresses the compressible element against the shoulder to expand the element radially outward and produce a first seal with a surrounding surface. A swellable element (180) also disposed on the body is swellable in the presence of an agent and expands radially outward to produce a second seal with the surrounding surface.