We consider fluid perturbations close to the 'phantom divide' characterised by p = -rho and discuss the conditions under which divergencies in the perturbations can be avoided. We find that the behaviour of the perturbations depends crucially on the prescription for the pressure perturbation delta-p. The pressure perturbation is usually defined using the dark energy rest-frame, but we show that this frame becomes unphysical at the divide. If the pressure perturbation is kept finite in any other frame, then the phantom divide can be crossed. Our findings are important for generalised fluid dark energy used in data analysis (since current cosmological data sets indicate that the dark energy is characterised by p ~ -rho so that p < -rho cannot be excluded) as well as for any models crossing the phantom divide, like some modified gravity, coupled dark energy and braneworld models. We also illustrate the results by an explicit calculation for the 'Quintom' case with two scalar fields.