The Seebeck coefficient S of the cuprate YBa2Cu3Oy is measured in magnetic fields large enough to suppress superconductivity, at hole dopings p ¼ 0.11 and p ¼ 0.12, for heat currents along the a and b directions of the orthorhombic crystal structure. For both directions, S=T decreases and becomes negative at low temperature, a signature that the Fermi surface undergoes a reconstruction due to broken translational symmetry. Above a clear threshold field, a strong new feature appears in Sb, for conduction along the b axis only. We attribute this feature to the onset of 3D-coherent unidirectional charge-density-wave modulations seen by x-ray diffraction, also along the b axis only. Because these modulations have a sharp onset temperature well below the temperature where S=T starts to drop towards negative values, we infer that they are not the cause of Fermi-surface reconstruction. Instead, the reconstruction must be caused by the quasi-2D bidirectional modulations that develop at significantly higher temperature. The unidirectional order only confers an additional anisotropy to the already reconstructed Fermi surface, also manifest as an in-plane anisotropy of the resistivity.