B. Blackadar recently proved that any full corner
p
A
p
pAp
in a unital C*-algebra
A
A
has K-theoretic stable rank greater than or equal to the stable rank of
A
A
. (Here
p
p
is a projection in
A
A
, and fullness means that
A
p
A
=
A
ApA=A
.) This result is extended to arbitrary (unital) rings
A
A
in the present paper: If
p
p
is a full idempotent in
A
A
, then
sr
(
p
A
p
)
≥
sr
(
A
)
\operatorname {sr} (pAp)\ge \operatorname {sr}(A)
. The proofs rely partly on algebraic analogs of Blackadar’s methods and partly on a new technique for reducing problems of higher stable rank to a concept of stable rank one for skew (rectangular) corners
p
A
q
pAq
. The main result yields estimates relating stable ranks of Morita equivalent rings. In particular, if
B
≅
End
A
(
P
)
B\cong \operatorname {End}_{A}(P)
where
P
A
P_{A}
is a finitely generated projective generator, and
P
P
can be generated by
n
n
elements, then
sr
(
A
)
≤
n
⋅
sr
(
B
)
−
n
+
1
\operatorname {sr}(A)\le n{\cdot }\operatorname {sr}(B)-n+1
.