  Employing the graded versions of the Yang-Baxter equation and the reflection
equations, we construct two kinds of integrable impurities for a small-polaron
model with general open boundary conditions: (a) we shift the spectral
parameter of the local Lax operator at arbitrary sites in the bulk, and (b) we
embed the impurity fermion vertex at each boundary of the chain. The
Hamiltonians with different types of impurity terms are given explicitly. The
Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are
constructed by means of the quantum inverse scattering method. In addition, we
discuss the ground-state properties in the thermodynamic limit.
