We present two variants of state-specific multi-reference coupled electron-pair type approximants (SS-MRCEPA) of our recently formulated state-specific multi-reference coupled-cluster (SS-MRCC) theory. Just like the parent SS-MRCC theory, these are formulated with a complete active space. and are rigorously size-extensive and size-consistent. They also bypass the intruder problem very efficiently. The efficacy of the methods is illustrated with the computation of the ground state potential energy surface of the trapezoidal H4 model. where the ground state requires a two-determinantal model space and the effective hamiltonian methods face intruders. (C) 2002 Elsevier Science B.V. All rights reserved.