The minimal energy of the nonrelativistic one-electron Pauli-Fierz model within the class of quasifree states is studied. It is shown that this minimum is unchanged if one restricts the variation to pure quasifree states, which simplifies the variational problem considerably. Existence and uniqueness of minimizers are established under the assumption of infrared and ultraviolet cutoffs, as well as, a sufficiently small coupling constant and a small momentum of the dressed electron. This is joint work with S. Breteaux and T. Tzaneteas and with S. Breteaux, H.K. Knoerr, and E. Menge.