The compound wire-tap channel is studied, which is based on Wyner's wire-tap model with both the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states. No matter which states occur for the two channels, the source wishes to guarantee that the destination decodes its message successfully and that the wire-tapper does not obtain the source message. The semideterministic compound wire-tap channel is first studied, in which the channel from the source to the destination is deterministic and has only one state. The secrecy capacity is obtained. An example parallel Gaussian compound wire-tap channel is then studied, in which both channels have two states. Three schemes are studied, and it is shown that introducing randomness either into the source message or into the encoder achieves the maximal secrecy degree of freedom. Both channels studied in this paper demonstrate that creating an auxiliary input, and hence adding a prefix channel from this auxiliary input to the actual channel input, improves the secrecy rate.