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Spring discharge often responds to rainfall with a rapid increase followed by a slower recession, and the mode of recession is often exponential-like. We propose a new model of the response of spring discharge to rainfall based on the square law for turbulent conduit flow. The new non-exponential model is compared against the exponential model under specific constraints. A hydrograph of St. Marks River in Florida is used to illustrate that when the change in "sinkhole head" (defined as the hydraulic head at the upstream end of the karst conduit connected to the spring) is relatively small, the solution of the new model is close to that of the exponential model, which extends the validity and application of the exponential solution. When the change in sinkhole head is very large, the solutions from the two models clearly differ from each other. Limitations of the non-exponential model are analyzed by simulation of a hydrograph observed downstream of Wakulla Springs. It is concluded that both solutions are applicable when spring response is smaller than or comparable to the base flow, but are nonphysical when the response is much larger than the base discharge. Published by Elsevier B.V.