Insulin secretion rate (ISR) in vivo is reconstructed by deconvolution from plasma concentration of C-peptide (CP), a peptide with linear kinetics which is co-secreted with insulin but is not extracted by the liver. Deconvolution requires the knowledge of the CP impulse response. A two-exponential (2E) model is usually chosen to describe the CP impulse response but a one-exponential (1E) model is also used in the literature. The purpose here is to discuss the domain of validity of the 1E model in reconstructing the ISR by deconvolution. In particular, we show that the 1E model can be reliably used only if the ISR spectrum is concentrated in a narrow frequency band and a suitable input is designed for its identification.