Employing the graded versions of the Yang-Baxter equation and the reflectio
n equations, we construct two kinds of integrable impurities for a small-po
laron model with general open boundary conditions: (a) we shift the spectra
l 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 H
amiltonians with different types of impurity terms are given explicitly. Th
e Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, a
re constructed by means of the quantum inverse scattering method. In additi
on, we discuss the ground-state properties in the thermodynamic limit.