Lifting units in clean rings

Let R be a clean ring with an ideal I such that R/I is semiperfect and K0(I) is torsion-free. We prove that, under some mild conditions, units in R/I can be lifted to units in R. This implies that the matrix ring Mn(R) over Bergmanʼs example of a non-clean exchange ring R is not clean, for every n. We also obtain some other results concerning lifting units in clean rings.