For an almost complex structure J on U C R4 pseudo-holomorphically fibered over C a J holomorphic curve C C U can be described by a Weierstrass polynomial. The J-holomorphicity equation descends to a perturbed -operator on the coefficients; the operator is typically (0, 2/m)-Holder continuous if m is the local degree of C over C. This sheds some light on the problem of parametrizing pseudo-holomorphic deformations of J-holomorphic curve singu larities.