  Conformal field theories with sl(2)_{-1/2} symmetry are studied with a view
to investigating logarithmic structures. Applying the parafermionic coset
construction to the non-logarithmic theory, a part of the structure of the
triplet model is uncovered. In particular, the coset theory is shown to admit
the triplet W-algebra as a chiral algebra. This motivates the introduction of
an augmented sl(2)_{-1/2}-theory for which the corresponding coset theory is
precisely the triplet model. This augmentation is envisaged to lead to a
precise characterisation of the "logarithmic lift" of the non-logarithmic
sl(2)_{-1/2}-theory that has been proposed by Lesage et al.
