The charge density wave in the high-temperature superconductor YBa2Cu3O7−x (YBCO) is now known to have two different ordering tendencies differentiated by their c-axis correlations. These correspond to ferro-(F-CDW) and antiferro-(AF-CDW) couplings between CDW in neighbouring CuO2 bilayers. This discovery has prompted a number of fundamental questions. For example, how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use high-energy x-ray diffraction to study YBa2Cu3O6.67 as a function of magnetic field and temperature. We show that regions of the sample with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a weak or fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is furthermore concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations have an important impact on superconducting and normal state properties of underdoped YBCO. * S.Hayden@bristol.ac.uk † johan.chang@physik.uzh.ch been realized [11][12][13][14]. These correspond to different ordering patterns along the c-axis [11,12]. Magnetic field (or uniaxial stress) induces an in-phase "ferro-coupled" CDW (F-CDW) along the b-axis [12, 13] on top of the original out-of-phase bi-axial "antiferro-coupled" CDW (AF-CDW) order. Quenched disorder, that in YBCO is naturally introduced through imperfections in the chain layer, may have important implications for the CDW order [13,15,16]. It is believed that disorder locally favors the AF-CDW order and that the evolution of the CDW correlations with magnetic field may be understood as a cross-over transition in which the CDW coupling along the c-axis varies [12,16].More recently, the case where competing tendencies towards CDW and SC order in the presence of topological defects due to quenched disorder and of vortices in the SC state has been considered [15]. It was demonstrated theoretically, that a "fragile" SC state can occur at low temperatures and at high magnetic field. This state is based on regions in which the CDW order is weakened due to defects where locally superconducting halos can form. These regions then can couple to form a state with global SC phase coherence. Given the richness of theoretical possibilities when superconductivity competes with arXiv:1909.09359v1 [cond-mat.supr-con]