A bend-limiting conduit controls the curvature of a catenary riser extending from the seafloor as it enters the centerwell of a spar-type offshore platform through the keel of the platform. The conduit has a bore dimensioned to receive the riser, and it extends from an upper end constrained within the keel to a lower end disposed below the keel. The conduit has increasing flexibility and weight per unit length from the upper end to the lower end, which results in a lateral load being applied to the riser as it passes through the conduit, thereby causing a gentle and gradual transition in the riser from a curved configuration at the lower end of the conduit, to a straight configuration as it emerges from the upper end of the conduit.