  We derive a numerical criterion for J-holomorphic curves in 4-dimensional
symplectic cobordisms to achieve transversality without any genericity
assumption. This generalizes results of Hofer-Lizan-Sikorav and
Ivashkovich-Shevchishin to allow punctured curves with boundary that generally
need not be somewhere injective or immersed. As an application, we combine this
with the intersection theory of punctured holomorphic curves to prove that
certain geometrically natural moduli spaces are globally smooth orbifolds,
consisting generically of embedded curves, plus unbranched multiple covers that
form isolated orbifold singularities.
