This letter shows that the effective permittivity ε for those metamaterials so far used to obtain a left-handed medium, consisting of 0.003 cm thick Cu strip wires, is dominated by the imaginary part of ε at 10.6–11.5 GHz frequencies. This is the region of a bandpass filter for microwaves, and therefore there is no propagation since the wave is inhomogeneous inside the medium. We compare with results of Shelby et al. [Appl. Phys. Lett. 78, 489 (2001)], and find that those are in error by ten orders of magnitude of the transmitted power. Also, from finite-difference time-domain calculations using the actual permittivity value of the Cu wires, we demonstrate that when the structure contains thicker wires, the losses are then reduced and the negative part of the permittivity dominates. Since the thickness of the wires is critical for the realization of a good transparent left-handed material, we propose that the strip wires should have thickness of 0.07–0.1 cm and the split ring resonators should be 0.030–0.06 cm thick.