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Abstract The elevation of natural river levees can vary considerably along the length of a river, and low‐lying features such as secondary floodplain channels allow for hydrologic exchange between a river and its floodplain over a range of discharges. This hydrologic, “river‐floodplain connectivity” plays a role in attenuating flood waves and transporting fluvial material to floodplain ecosystems. However, flood wave attenuation and transport are also limited by the available storage provided by floodplains. In this study, we explore the combined controls of river‐floodplain connectivity and floodplain width on flood wave attenuation and transport, and how those controls change as flood magnitude increases. We develop idealized river‐floodplain models based on the geometry of the lower Trinity River in Texas, USA, varying floodplain width, peak discharge, and degree of river‐floodplain connectivity, which we prescribe by varying the width of a secondary channel connecting the river to the floodplain. We show that attenuation transitions from connectivity‐limited to storage‐limited as discharge increases. Secondary channel conveyance allows for floodplain inundation at lower discharges, but also fills the floodplain faster and, for larger floods, can cause higher flood peaks downstream. Greater secondary channel conveyance and wider floodplains increase fluxes to the floodplain, but secondary conveyance allows the floodplain to drain faster while wider floodplains have longer average residence times. This study presents a framework for understanding how secondary channel conveyance and floodplain width combine to modulate lateral flow exchange, residence times, and flood wave attenuation, and can guide successful management of river systems and future restoration efforts.