We introduce and investigate the concept of frozen partial co-clones. Our main motivation for studying frozen partial co-clones is that they, have important applications in complexity analysis of constraints. The frozen partial co-clones lie between the co-clones and partial co-clones in the sense that the partial co-clone lattice is a refinement of the frozen partial co-clone lattice, which in turn is a refinement of the co-clone lattice. We concentrate on the Boolean domain. and determine large parts of the frozen partial co-clone lattice.