Different pole structures in line shapes of the X(3872)

We introduce a near-threshold parameterization that is more general than the effective-range expansion up to and including the effective range because it can also handle a near-threshold zero in the D-0(D) over bar*(0) S-wave. In terms of it we analyze the CDF data on inclusive p (P) over bar scattering to J/psi pi(+)pi(-), and the Belle and BaBar data on B decays to K J/psi pi(+) pi(-) and KD (D) over bar*(0) around the D-0(D) over bar*(0) threshold. It is shown that data can be reproduced with similar quality for X(3872) being a bound and/or a virtual state. We also find that X(3872) might be a higher-order virtual-state pole (double or triplet pole), in the limit in which the small D*(0) width vanishes. Once the latter is restored the corrections to the pole position are non-analytic and much bigger than the D*(0) width itself. The X(3872) compositeness coefficient in D-0(D) over bar*(0) ranges from nearly 0 up to 1 in the different scenarios.