Let
A
A
be a unital operator algebra. We prove that if
ρ
\rho
is a completely bounded, unital homomorphism of
A
A
into the algebra of bounded operators on a Hilbert space, then there exists a similarity
S
S
, with
‖
S
−
1
‖
⋅
‖
S
‖
=
‖
ρ
‖
c
b
\left \| {{S^{ - 1}}} \right \| \cdot \left \| S \right \| = {\left \| \rho \right \|_{cb}}
, such that
S
−
1
ρ
(
⋅
)
S
{S^{ - 1}}\rho ( \cdot )S
is a completely contractive homomorphism. We also show how Rota’s theorem on operators similar to contractions and the result of Sz.-Nagy and Foias on the similarity of
ρ
\rho
-dilations to contractions can be deduced from this result.