  In a two-Higgs-doublet model (2HDM), at the vicinity of the alignment limit,
the extra contributions to the couplings of the SM-like Higgs with other
particles can be subdominant to the same coming from the six dimensional
operators. In this context, we revisit the alignment limit itself. It is
investigated to what extent these operators can mask the actual alignment in a
2HDM. The bosonic operators which rescale the Higgs kinetic terms can lead to
substantial change in the parameter space of the model. We find that some other
bosonic operators, which are severely constrained from the electroweak
precision tests, can also modify the parameter space of 2HDM due to their
anomalous momentum structures. A particular kind of Little Higgs model is
explored as an example of 2HDM effective field theory in connection with 2HDM
alignment. Choosing a suitable benchmark point in a Type-II 2HDM, we highlight
the possibility that the exact alignment limit is ruled out at 95% CL in
presence of such operators.
