  Recently, it was found that certain 4d $\mathcal{N}=1$ Lagrangians experience
supersymmetry enhancement at their IR fixed point, thereby giving a Lagrangian
description for a plethora of Argyres-Douglas theories. A generic feature of
these Lagrangians is that a number of gauge invariant operators decouple (as
free fields) along the RG-flow. These decoupled operators can be naturally
taken into account from the beginning itself by introducing additional gauge
singlets (sometimes called `flipping fields') that couple to the decoupled
operators via appropriate superpotential terms. It has also been checked that
upon dimensionally reducing to 3d, the $(A_1,A_{2n-1})$ type Lagrangians only
produce the expected behavior when flipping fields are included in the
Lagrangian. In this paper we further investigate the role of flipping fields
and find an example where the expected necessity of including the flipping
fields in the dimensionally reduced Lagrangians seems to get violated. In the
process we find two new dual Lagrangians for the so called 3d $T[SU(2)]$
theory.
