Ocean-bottom seismograph and multichannel streamer wide-angle seismic data are jointly analysed and compared with reflection images, bathymetric maps and potential field data, to reveal the detailed structure of layer 2 of the oceanic crust formed at the intermediate spreading Costa Rica Rift (CRR). Separate modelling of each wide-angle data set independently reveals a gradual increase in P-wave velocity with distance (hence crustal age) from the ridge axis, with a model derived from their joint inversion, in turn, displaying a pattern of shorter-wavelength structural complexity in addition to a background flow-line trend. Normalizing against a ridge-located reference velocity–depth model reveals that, off-axis, velocity perturbations are correlated with trends in basement roughness and uplift; regions of rougher and uplifted basement correlate with slower layer 2 velocity, <0.5 km s−1 faster than at the ridge axis, and thinner sediment cover, while smoother basement and locations where sediment cover forms a continuous seal over the oceanic basement, are mirrored by regions of relatively higher velocity, 1.0–1.4 km s−1 faster than at the CRR. These velocity variations are interpreted to reflect periodic changes in the degree of magma supply to the ridge axis. Using a combination of global and shipboard magnetic data, we derive a spreading history model for the CRR which shows that, for the past 5 Ma, spreading has been asymmetric. Comparing the seismic model structure with variations in full spreading rate over this period, reveals a correlation between periods of slower spreading and slower layer 2 velocity, basement roughness and uplift, and faster spreading, higher velocity and smoother basement structure. Zones of slower velocity also correlate with lows in the residual mantle Bouguer anomaly, interpreted as most likely reflecting corresponding regions of lower density in the lower crust or upper lithospheric mantle. Using ODP borehole 504B as ground-truth, we show that periods of faster spreading are associated with phases of magmatic accretion, interspersed by phases of increased asymmetric tectonic extension that likely facilitates fluid flow to the deeper crust and results in metamorphic alteration, manifest as the modelled density anomalies. Overall, our study shows that the mode of CRR crustal formation is sensitive to relatively small changes in full spreading rate within the range of 50–72 mm yr−1, that tips the balance between magmatic and magma-dominated crustal formation and/or tectonic stretching, as characterized by significant variation in the fabric and physical properties of layer 2. We further hypothesize that this inherited structure has a direct influence on the subsequent evolution of the crust through secondary alteration. We conclude that descriptive phrases like ‘ocean crust formed at an intermediate-spreading rate’ should no longer be used to describe an actual crustal formation process or resulting crustal structure as, over the full range of intermediate spreading rates, a fine tipping-point dictates an episodic transition between primarily magmatic accretion and magma-dominated crustal formation coupled with enhanced faulting, with their asymmetry recorded in either ridge flank.