The simplest version of the Maskit-Klein combination theorems concerns the action of a free product of two finite subgroups of
P
S
L
(
2
,
C
)
PSL(2,{\mathbb C})
on the Riemann sphere
C
^
\hat {\mathbb C}
, when these subgroups have fundamental domains whose interiors together cover
C
^
\hat {\mathbb C}
. We prove an analogous combination theorem for covering correspondences of rational maps, making use of Douady and Hubbard’s Straightening Theorem for polynomial-like maps to describe the structure of the limit sets. We apply our theorem to construct holomorphic correspondences which are matings of polynomial maps with Hecke groups
C
p
∗
C
q
C_p*C_q
, and we show how it may also be applied to the analysis of separable correspondences.